Treatment planning for aligning a patient&#39;s teeth

ABSTRACT

Methods and systems (including software) for creating a treatment plan to align a patient&#39;s teeth using a plurality of removable aligners to be worn in sequential stages. These methods and systems may generate a plurality of potential treatment plan variations. Each variation may be optimized to best address the user&#39;s treatment goals, as well as approximating as closely as possible an ideal or target final position.

CROSS REFERENCE TO RELATED APPLICATIONS

This patent application is a continuation of U.S. patent applicationSer. No. 17/406,071, filed Aug. 18, 2021, titled “AUTOMATIC TREATMENTPLANNING,” which is a continuation of U.S. patent application Ser. No.16/178,491, filed Nov. 1, 2018, titled “AUTOMATIC TREATMENT PLANNING,”now U.S. Patent Application Publication No. 2019/0175303, which claimspriority to U.S. Provisional Patent Application No. 62/580,432, filed onNov. 1, 2017, titled “REAL-TIME, INTERACTIVE DENTAL TREATMENT PLANNING;”U.S. Provisional Patent Application No. 62/580,427, filed on Nov. 1,2017, titled “AUTOMATIC TREATMENT PLANNING;” and U.S. Provisional PatentApplication No. 62/692,551, filed on Jun. 29, 2018, titled “AUTOMATICTREATMENT PLANNING;” each of which is herein incorporated by referencein its entirety.

INCORPORATION BY REFERENCE

All publications and patent applications mentioned in this specificationare herein incorporated by reference in their entirety to the sameextent as if each individual publication or patent application wasspecifically and individually indicated to be incorporated by reference.

FIELD

Treatment planning for orthodontic treatment using a series ofpatient-removable appliances to reposition the teeth.

BACKGROUND

Orthodontic and dental treatments using a series of patient-removableappliances (e.g., “aligners”) are very useful for treating patients, andin particular for treating malocclusions. Treatment planning istypically performed in conjunction with the dental professional (e.g.,dentist, orthodontist, dental technician, etc.), by generating a modelof the patient's teeth in a final configuration and then breaking thetreatment plan into a number of intermediate stages (steps)corresponding to individual appliances that are worn sequentially. Thisprocess may be interactive, adjusting the staging and in some cases thefinal target position, based on constraints on the movement of the teethand the dental professional's preferences. Once the final treatment planis finalized, the series of aligners may be manufactured correspondingto the treatment planning.

This treatment planning process may include many manual steps that arecomplex and may require a high level of knowledge of orthodontic norms.Further, because the steps are performed in series, the process mayrequire a substantial amount of time. Manual steps may includepreparation of the model for digital planning, reviewing and modifyingproposed treatment plans (including staging) and aligner featuresplacement (which includes features placed either on a tooth or on analigner itself). These steps may be performed before providing aninitial treatment plan to a dental professional, who may then modify theplan further and send it back for additional processing to adjust thetreatment plan, repeating (iterating) this process until a finaltreatment plan is completed and then provided to the patient.

The methods and apparatuses described herein may improve treatmentplanning, including potentially increasing the speed at which treatmentplans may be completed, as well as providing greater choices and controlto the dental professional, and allowing improved patient involvement inthe treatment planning process.

SUMMARY OF THE DISCLOSURE

Described herein are orthodontic and/or dental treatment planningmethods and apparatuses. In particular, described herein are methods ofplanning a dental and/or orthodontic treatment. Any of the methods andapparatuses described herein may pre-calculate a plurality of potentialtreatment plan variations including all of the staging and various,potentially alternative, final configurations and display them inparallel. A very large number of such plans may be generated at once(e.g., as a large set or array) quickly and reviewed in real time ornear real-time. A treatment plan may include a plurality of differentstages during which the patient's teeth are moved from an initialposition to a final position; a dental aligner (e.g., a shell aligner)or other orthodontic device may be made to correspond to each stage, andworn in the sequence defined by the treatment plan to move the patientsteeth from their initial position to a final position.

The methods and apparatuses described herein allow for the concurrentgeneration of a large number of treatment plan variations in which eachvariation is optimized to best address the dental professional's (and insome cases, the patient's) treatment goals, as well as approximating asclosely as possible an ideal or target final position. Also describedherein are orthodontic and/or dental treatment planning methods andapparatuses that allow a dental professional (e.g., a “user”) and/or apatient to form, modify, and select a treatment plan from a plurality ofdifferent treatment plans, in real time.

For example, a dental professional may make a model (e.g., a digitalmodel or scan, and/or a physical model, which may subsequently bedigitized) and send it to a remote site (e.g., a laboratory) wheremultiple options for treatment plans may be generated. The model may betransmitted along with one or more of: treatment preferences from thedental professional specific to the patient, treatment preferencesspecific for the particular dental professional that may be applied toall patient's associated with that dental professional, and/or anindication of what clinical product(s) (e.g., orthodontic product)should be used to move the patient's teeth. This data may be used asinputs to generate the plurality of optional treatment plans, will bedescribed in greater detail below. The resulting multiple treatmentplans (which may collectively be referred to as an array of treatmentplans, a set of treatment plans, or a collection of treatment plans ortreatment plan variations) may then be transmitted back to the dentalprofessional for interactive display, selection and/or modification bythe dental professional and/or patient. Note that each treatment planmay have multiple stages, wherein at each stage of that treatment planan aligner may be worn for a predetermined period of time; alternativelyor additionally in some variations one or more stage may includeorthodontic/dental manipulations (e.g., tooth removal, interproximalreduction, etc.) on the patient's teeth.

The methods and apparatuses described herein allow the rapid andcreation of a large number of full treatment plans specific andcustomized to a patient setting froth an orthodontic and/or dental planfor beneficially modifying the subject's dentition, including inparticular, moving (e.g., aligning, straightening, etc.) the patientsteeth and/or resolving orthodontic issues specific to the patient.Traditionally, only a single orthodontic treatment plan was provided toa user and/or patient, in which the patient's dentition was modifiedfrom the patients initial dental position to a final dental position,often a comprehensive final position of the patient's teeth. In generala treatment plan may include a series of patient-removable appliances toreposition the teeth, and some indication of the duration of time eachappliance (“aligner”) is to be worn. At each stage of the treatmentplan, one or more (or all) of the patient's teeth maybe moved relativeto the prior stage, until the teeth are in a target configuration; oncein the target configuration, the final stage(s) may optionally be aretainer (or multiple retainers) to maintain the target configurationfor some retaining duration. Any number of stages may be used. In somevariations the treatment plan may also indicate one or moredental/orthodontic procedures to be performed at that stage (e.g.,interproximal reduction, tooth extraction, etc.).

The apparatuses (e.g., systems, devices, etc. including software,firmware and hardware), which may include treatment plan solvers, andmethods described herein may rapidly generate a plurality of differenttreatment plans, each customized to the patient. These method andapparatuses may take into account the treatment preferences of thedental professional and/or patient, and/or the types and constraints ofavailable appliances (aligners) when generating these treatment plans.Alternatively plans in which one or more of these parameters aredifferent may be generated, allowing direct comparison between a largenumber of alternative plans. Typically generating even a singletreatment plan has proven complex and time intensive. Manual techniqueshave been used for treatment planning and may require many hours or daysto complete. Automation has also proven difficult, particularly whenestimating or preventing collisions between teeth during the treatment.The methods and apparatuses described herein may provide an extremelyfast and effective way to generate (and in some cases generateconcurrently or nearly concurrently) a large number of different andtherapeutically viable treatment plans. Treatment plans may be generatedwith no or minimal technician or dental professional oversight required.In some variations of the methods and apparatuses described herein morethan 3 (e.g., more than 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 25,30, 35, 40, 45, 50, 60, 70, 80, 90, 100, 125, 150, 175, 200, 250, 300,350, 400, 500, etc.) complete treatment plans, each including a varietyof stages and corresponding tooth position and/or appliance (e.g.,aligner) configuration (in some variations the tooth position at eachstage may be used to generate a dental appliance).

For example, described herein are automated methods of creating aplurality of dental/orthodontic treatment plans, as well as devices forperforming them (e.g., treatment plan solvers). An automated method ofcreating a plurality of variations of treatment plans to align apatient's teeth using a plurality of removable aligners to be worn insequential stages may include: (a) specifying a set of treatmentpreferences and a set of treatment details (the treatment preferencesand treatment details may be automatically or manually specified); (b)automatically determining a treatment plan based on the specifiedtreatment preferences and treatment details, by: collecting (e.g.,receiving, forming, gathering, downloading, and/or accessing), in aprocessor: a digital model of a patient's teeth, and accessing, by theprocessor, the set of treatment preferences, a comprehensive finalposition of the patient's teeth, and the set of treatment details;selecting a plurality of numerically expressed treatment targets from amemory accessible to the processor, based on the set of treatmentdetails, the set of treatment preferences and the comprehensive finalposition of the patient's teeth; combining the plurality of numericallyexpressed treatment targets to form a single numerical function;selecting a plurality of numeric limits on the single numerical functionbased on the set treatment preferences; minimizing the single numericalfunction subject to the plurality of numeric limits to get a solutionvector including all stages forming the treatment plan; and mapping thesolution vector to a treatment plan, wherein the treatment plan includesa final tooth position that is different from the comprehensive finalposition of the patient's teeth (c) adding the treatment plan to anarray of treatment plans; and (d) modifying one or more of the treatmentdetails or treatment preferences and repeating steps (b)-(d) at leastonce. The method may also include adding metadata identifying thetreatment details or treatment preferences to each treatment plan sothat the array of treatment plans includes the identifying metadata. Themetadata does not need to indicate all of the treatment details ortreatment preference information, but may include just a subset of it,such as just those parameters that are different from the othertreatment plans (e.g., number of stages, use of IPR, etc.).

In any of the methods and apparatuses described herein, minimizing thesingle numerical function subject to the plurality of numeric limits toget a solution vector including all stages forming the treatment planmay include estimating collisions between adjacent teeth. Thus, any ofthese apparatuses may include a collision detector, and particular acollision detector that determines the magnitude and/or velocity ofcollisions (or separation, which is negative collision) between teeth.The use of very rapid collision detection/detectors may enhance the rateand efficiency of the methods and apparatuses for treatment planningdescribed herein; automated collision detection methods and systems(collision detectors) are also described in greater detail herein.

In some variations the method may also include an automated analysis ofthe final stage tooth position to determine the amount or level ofcorrection of the patient's malocclusions achieved. This treatmentoutcome information may be added, e.g., as metadata, to the array oftreatment plans.

Also described herein are methods and apparatuses for generating ortranslating user-specific treatment preferences. Dental professionals(e.g., users) may provide comments, requests and feedback on treatmentplans across many cases. The methods and apparatuses described hereinmay interpret these comments, request and feedback, as treatmentpreferences. For example, these treatment preferences may includepreferences with respect to modifying the patient's teeth (e.g., IPR,including which teeth to perform IPR on, what stage of treatment toperform IPR, etc.), the use of attachments (to use/not to use, where toplace them, when to use them), and the like. The methods and apparatusesdescribed herein may build and use a database of such user-specifictreatment preferences. This database may be updated and modified as theuser performs additional cases. Further, this database may be accessedto generate a treatment plan (or an array of treatment plans), asdescribed herein.

For example, an automated and customized method for creating anorthodontic treatment plan of a patient's teeth for a specified dentalprofessional may include: collecting (e.g., receiving, forming,gathering, downloading, and/or accessing), in a treatment planoptimizing engine (e.g., a processor), a set of combined treatmentpreferences specific to the specified dental professional, wherein theset of combined treatment preferences comprises a first set of rulesconverted from a set of textual instructions from the specified dentalprofessional into a domain-specific language specific to the specifieddental professional, further wherein the textual instructions compriseunscripted instructions, and a second set of rules converted from a setof scripted instructions from the specified dental professional, whereinthe scripted instructions comprise responses from a script of predefinedchoices; receiving, in the treatment plan optimizing engine, a digitalmodel of the patient's teeth; and generating, with the treatment planoptimizing engine, a treatment plan for the patient's teeth using theset of combined treatment preferences and the digital model of thepatient's teeth. The different treatment properties may comprise one ormore of: interproximal reduction (IRR), extraction, and alignerattachments.

The scripted instructions from the specified dental professional may bespecific to the patient's teeth. The textual instructions may bespecific to the patient's teeth, and/or the textual instructions may beextracted from a plurality of different prior cases by the specifieddental professional.

The textual instructions may comprise instructions on one or more of,for example, staging of interproximal reduction and positions ofattachments. Any other treatment preference may be included as atextural instruction.

In general, any of the methods may include updating the domain-specificlanguage specific to the specified dental professional, and/or storingthe domain-specific language specific to the specified dentalprofessional in a remote database accessible by the treatment planoptimizing engine. Any of these methods may include automaticallygenerating the domain-specific language specific to the specified dentalprofessional, or manually converting textual instructions into thedomain-specific language specific to the specified dental professional.

Any of these methods may include identifying the specified dentalprofessional to the treatment plan optimizing engine; for example, thedental professional may be identified by an identifier (dentalprofessional identifier) such as name (last, first, etc.), practicename, number, etc. The identifiers described herein may uniquelyidentify the dental professional.

As described in greater detail herein, typically generating thetreatment plan comprises determining a final position of the patient'steeth, and determining each of a plurality of stages of tooth movementbased on the combined treatment preferences, wherein each stagecomprises a dental aligner.

For example, described herein are automated and customized method forcreating an orthodontic treatment plan of a patient's teeth for aspecified dental professional, the method comprising: receiving, in aprocessor, a set of scripted instructions from a specified dentalprofessional, wherein the scripted instructions comprise responses froma script of predefined choices; receiving in the processor, a set oftextual instructions from the specified dental professional, wherein thetextual instructions comprise unscripted instructions; converting theset of textual instructions into a domain-specific language specific tothe specified dental professional, wherein the domain-specific languagecomprises a first set of rules; converting the set of scriptedinstructions into a second set of rules; combining the first set orrules and the second set of rules into a set of combined treatmentpreferences; and passing the set of combined treatment preferences to atreatment plan optimizing engine, wherein the treatment plan optimizingengine generates a treatment plan using the combined treatmentpreferences.

Any of these methods may also include accessing, by the processor, adatabase of the domain-specific language corresponding to the specifieddental professional.

Any of the methods described herein may be performed by an apparatusconfigured and/or adapted to perform them. For example, also describedherein are non-transitory computer-readable storage media having storedthereon, computer-executable instructions that, when executed by acomputer, cause the computer to automatically create an orthodontictreatment plan of a patient's teeth customized for a specified dentalprofessional by: receiving, in a treatment plan optimizing engine, a setof combined treatment preferences specific to the specified dentalprofessional, wherein the set of combined treatment preferencescomprises a first set of rules converted from a set of textualinstructions from the specified dental professional into adomain-specific language specific to the specified dental professional,further wherein the textual instructions comprise unscriptedinstructions, and a second set of rules converted from a set of scriptedinstructions from the specified dental professional, wherein thescripted instructions comprise responses from a script of predefinedchoices; receiving, in the treatment plan optimizing engine, a digitalmodel of the patient's teeth; and generating, with the treatment planoptimizing engine, a treatment plan for the patient's teeth using theset of combined treatment preferences and the digital model of thepatient's teeth.

As mentioned above, also described herein are methods and apparatuses(e.g., systems, devices, etc., including software) for automaticallydetecting and/or estimating collisions between teeth. These methods andapparatuses may provide an approximation of the magnitude and/orvelocity of collisions between teeth. The magnitude and velocity of acollision may be expressed as a vector or a scalar value or values. Thevelocity may be velocity in each of a plurality of axes, such as threetranslational axes (x, y, z) and three rotational axes (pitch, roll,yaw). In some variations the magnitude and velocity of collisions may bedetermined between all adjacent pairs of teeth. The magnitude of acollision may be positive (e.g., indicating the depth of collision) ornegative (indicating separation or spacing between teeth).

Although the automated collision detection systems and methods describedherein may be particularly useful as part of automated method forgenerating treatment plans (e.g., as part of a treatment plan solver),they are not limited to this. It should be understood that the methodsand apparatuses described herein may also be used independently, or aspart of any other method or apparatus that may benefit from automaticand rapid detection of collision between two or more teeth.

For example, a method of automatically determining collisions betweenadjacent teeth may include: forming a digital model of a surface foreach tooth of a plurality of a patient's teeth by automatically packinga plurality of 3D shapes to approximate the surface for each tooth,wherein the 3D shapes each have a core that is a line segment or aclosed plane figure and an outer surface that is a constant radius fromthe core; forming, for the digital model of the surface for each tooth,a hierarchy of bounding boxes enclosing the plurality of 3D shapes;measuring, in the collisions detector, a magnitude and a velocity of acollision between adjacent teeth when the plurality of the patient'steeth are in a set of tooth positions by identifying colliding boundingboxes and determining the spacing or overlap between the 3D shapes boundby the colliding bounding boxes; and outputting the magnitude andvelocity of the collision between adjacent teeth corresponding to theset of tooth positions.

Any of the methods for automatically determining collisions may alsoinclude collection (e.g., receiving, downloading, accessing, etc.) a setof tooth positions. The tooth positions may correspond to the positionsof the teeth in space. In some variations the teeth may be arranged in acoordinate system (e.g., x, y, z) allowing relative positions of theteeth to be understood.

In general, in any of the methods and apparatuses for automaticallydetermining collisions (e.g., collision detectors) described herein, oneor more surfaces of the patient's teeth may be filled with the 3Dshapes. As used herein a 3D shape may refer to a shape having a corethat is a line or planar (including closed planar) figure, and an outer3D surface surrounding and extending from the core by a set radius, r.In some variations the 3D shapes are capsules, which have a core that isa line segment extending some length, L. The body of the 3D shape(capsule body) is elongated but rounded at the end, havingsemi-spherical ends. Any appropriate 3D shape, or combination of 3Dshapes may be used. These 3D shapes may exclude spheres, which typicallyhave a point at the core, surrounded by a surface at an outer radius. 3Dshapes having a core that is a line or a plane figure, and particularlyclosed plane figures (such as rectangles, circles, etc.) that formshapes having both linear and convex outer surfaces may work much betterthan simple spheres when filling tooth surfaces, which may be concave,convex, as well as flat in some regions.

In general, when automatically determining collision between two teeth,each of the two teeth being processed may be divided into portions, sothat just those surfaces of the portions of the teeth that face eachother need to be filled/modeled with the 3D shapes (e.g., capsules). Insome variations the teeth may be first divided in half, into a left halfand a right half, and only the sides of the teeth that face each otherneed to be processed. Thus, forming the digital model of the surface foreach tooth may include separately forming a left side and a right sideof each tooth. Thus, measuring the magnitude and velocity of thecollision between adjacent teeth may comprise identifying collisionsbetween adjacent left sides and right sides of the adjacent teeth.

In any of the collision detection methods and apparatuses describedherein, forming the digital surface of the surface for each tooth mayinclude automatically packing the plurality of 3D shapes to approximatethe surface. In some the surface (and/or the entire tooth volume, or aportion of the tooth volume, such as the left side/right side) may bemodeled by packing with a plurality of 3D shapes (e.g., capsules) thatare all the same shape and size, or different shapes and/or differentsize 3D shapes may be used. In processing to determine collisions(and/or spacing) between adjacent teeth, the closet capsules betweeneach of the two teeth may be determined by bounding boxes and one ormore numeric methods may be used to solve for the collision magnitude(which may be overlap/collision and be a positive magnitude value or maybe spacing and be a negative collision magnitude).

Thus, and of the methods and apparatuses for collision detectiondescribed herein may also include forming a hierarchy of bounding boxesaround the 3D shapes (e.g., capsules) forming the surface of the firsttooth and a second hierarchy of bounding boxes may be determined aroundthe 3D shapes (e.g., capsules) forming the surface of the second tooththat is adjacent to the first tooth. The use of a tiered hierarchy ofbounding boxes around the 3D shapes forming the surfaces allows for acomputationally rapid determination of which of the bounding boxes inthe hierarchy do and do not overlap/collide. At the lowest tier of thehierarchy each bounding box encloses a single 3D shape; each subsequenttier bound two adjacent bounding boxes, until the highest tier, whichbounds all of the bounding boxes around all of the 3D shapes. Formingthe hierarchy of bounding boxes may comprises, for example, forming ahierarchy in which bounding boxes of a lowest tier of the hierarchy eachenclose a single 3D shape, subsequent tiers of the hierarchy eachenclose adjacent bounding boxes or groups of bounding boxes, and ahighest tier of the hierarchy encloses all of the bounding boxes aroundthe 3D shapes forming the surface. When comparing the hierarchy ofbounding boxes, the comparison may start at the top of the hierarchy; ifthe top-tier hierarchy for each adjacent tooth surface does not collide,then none of the bounding boxes in the hierarchy will collide. Eachbranch of the first hierarchy (e.g., corresponding to the first toothsurface) may be compared with each branch of the second hierarchy (e.g.,corresponding to the second tooth surface) starting from the top tierand working down the hierarchy tiers; at any tier that there is nooverlap (e.g., collision, which may be detected by measuring theshortest distance between the bounding boxes at that tier) between twobranches, no further lower-tiered branches need to be examined. Once thelowest tier has been reached, the 3D shapes in the colliding boundingboxes may then be used to determine the collision magnitude andvelocity.

The magnitude of the collision between adjacent teeth may be measuredby, for example, determining the spacing or overlap between the 3Dshapes bound by the colliding bounding boxes to get the magnitude of thecollision. As just mentioned, measuring the magnitude and velocity ofthe collision between adjacent teeth may include starting from a toptier of the hierarchy of bounding boxes and proceeding down the tiers tothe lowest tier of the hierarchy of bounding boxes corresponding to eachadjacent tooth, comparing the branches at each tier between the twoadjacent teeth in order to identify colliding bounding boxes at thelowest tier of the hierarchy of bounding boxes. Once the collidingbounding boxes are determined, the shortest distance (the maximumoverlap) between the two 3D shapes (e.g., capsules) may becomputationally determined.

The velocity of the collision between adjacent teeth may be measured by‘jittering’ one or both of the colliding teeth relative to the other;for example, one of the 3D shape-filled teeth (or portion of the tooth)may be moved very slightly (e.g., between 0.001-0.0001 inch) in each ofone of the spatial axes (e.g., x, y, z, pitch, roll, yaw) anddetermining the change in the collision after each sequential movement.For example, by sequentially adjusting a position of a first 3D shape ofthe adjacent teeth by a small predetermined amount in each of aplurality of axes of the first tooth and determining the change inspacing or overlap between the 3D shapes bound by the bounding boxes toget the velocity of the collision for each of the corresponding axes.The change in collision/spacing magnitude following each change may beexpressed for that axes as the velocity (the time to achieve the changemay be assumed to be a set value, e.g., 1).

The velocity may be expressed as a single vector (e.g., the x, y, zdirection) and/or rotation; in some variations the velocity may beexpressed in each of the axes (three spatial and 3 rotational).Alternatively, in some variations, only the three spatial (or threerotational) axes are examined. The resulting collision magnitude andvelocity may be output, e.g., by outputting the magnitude and thevelocity for each of three spatial and three rotational axes. The output(magnitude, velocity or both magnitude and velocity) may be passed tothe treatment planning solver, or to any other system that the collisiondetector is part of, and/or it may be output (e.g., displayed, stored,transmitted, etc.) for independent use.

Also described herein are systems for automatically detecting collisionsbetween teeth. These systems may be referred to as collision detectorsand may include, for example: one or more processors; and a memorycoupled to the one or more processors, the memory configured to storecomputer-program instructions, that, when executed by the one or moreprocessors, perform a computer-implemented method comprising: forming adigital model of a surface for each tooth of a plurality of a patient'steeth by automatically packing a plurality of 3D shapes to approximatethe surface for each tooth, wherein the 3D shapes each have a core thatis a line segment or a closed plane figure and an outer surface that isa constant radius from the core; forming, for the digital model of thesurface for each tooth, a hierarchy of bounding boxes enclosing theplurality of 3D shapes; measuring, in the collisions detector, amagnitude and a velocity of a collision between adjacent teeth when theplurality of the patient's teeth are in a set of tooth positions byidentifying colliding bounding boxes and determining the spacing oroverlap between the 3D shapes bound by the colliding bounding boxes; andoutputting the magnitude and velocity of the collision between adjacentteeth corresponding to the set of tooth positions.

As mentioned above, any of these method of detecting collisions and/orcollision detectors may be included as part of a system or method forautomatically creating an orthodontic treatment plan of a patient. Forexample, a method of automatically creating an orthodontic treatmentplan for a patient may include: forming a digital model of a surface foreach tooth of a plurality of a patient's teeth by packing a plurality of3D shapes to approximate the surface for each tooth, wherein the 3Dshapes each have a core that is a line segment or a closed plane figureand an outer surface that is a constant radius from the core; forming,for the surface for each tooth of the plurality of the patient's teeth,a hierarchy of bounding boxes enclosing the plurality of 3D shapes;passing a set of tooth positions for the plurality of the patient'steeth from a treatment plan solver to a collision detector; measuring,in the collisions detector, a magnitude and a velocity of a collisionbetween adjacent teeth when the plurality of the patient's teeth are inthe set of tooth positions by identifying colliding bounding boxes anddetermining the spacing or overlap between the 3D shapes bound by thecolliding bounding boxes; and passing the magnitude and velocity of thecollision between adjacent teeth corresponding to the set of toothpositions to the treatment plan solver; and outputting, from thetreatment plan solver, one or more orthodontic treatment planscomprising a series of dental appliances for moving the patient's teeth.

A method of automatically creating an orthodontic treatment plan of apatient may include: collecting a digital model of a plurality of thepatient's teeth, wherein each tooth of the digital model is segmented;automatically packing a plurality of 3D shapes to approximate a surfacefor each tooth of the digital model, wherein the 3D shapes each have acore that is a line segment or a closed plane figure and an outersurface that is a constant radius from the core; forming, for thesurface for each tooth of the digital model, a hierarchy of boundingboxes enclosing the plurality of 3D shapes, wherein for each surface foreach tooth of the digital model, bounding boxes of a lowest tier of thehierarchy each enclose a single 3D shape, subsequent tiers of thehierarchy each enclose adjacent bounding boxes or groups of boundingboxes, and a highest tier of the hierarchy encloses all of the boundingboxes around the 3D shapes forming the surface; passing a set of toothpositions for the plurality of the patient's teeth from a treatment plansolver to a collision detector; measuring, in the collisions detector, amagnitude and a velocity of a collision between adjacent teeth when theplurality of the patient's teeth are in the set of tooth positions byidentifying colliding bounding boxes at the lowest tier of the hierarchyfor each of the adjacent teeth, determining the spacing or overlapbetween the 3D shapes bound by the bounding boxes to get the magnitudeof the collision, and sequentially adjusting a position of a first toothof the adjacent teeth by a small predetermined amount in each of aplurality of axes of the first tooth and determining the change inspacing or overlap between the 3D shapes bound by the bounding boxes toget the velocity of the collision for each of the corresponding axes;and outputting the magnitude and velocity of the collision betweenadjacent teeth corresponding to the set of tooth positions to thesolver; outputting, from the solver, one or more orthodontic treatmentplans comprising a series of dental appliances for moving the patient'steeth.

A system for automatically creating an orthodontic treatment plan of apatient may include: one or more processors; a treatment plan solveroperating on the one or more processors; a collision detector operatingon the one or more processors; and a memory coupled to the one or moreprocessors, the memory configured to store computer-programinstructions, that, when executed by the one or more processors, performa computer-implemented method comprising: forming a digital model of asurface for each tooth of a plurality of a patient's teeth by packing aplurality of 3D shapes to approximate the surface for each tooth,wherein the 3D shapes each have a core that is a line segment or aclosed plane figure and an outer surface that is a constant radius fromthe core; forming, for the surface for each tooth of the plurality ofthe patient's teeth, a hierarchy of bounding boxes enclosing theplurality of 3D shapes; passing a set of tooth positions for theplurality of the patient's teeth from a treatment plan solver to acollision detector; measuring, in the collisions detector, a magnitudeand a velocity of a collision between adjacent teeth when the pluralityof the patient's teeth are in the set of tooth positions by identifyingcolliding bounding boxes and determining the spacing or overlap betweenthe 3D shapes bound by the colliding bounding boxes; passing themagnitude and velocity of the collision between adjacent teethcorresponding to the set of tooth positions to the treatment plansolver; and outputting, from the treatment plan solver, one or moreorthodontic treatment plans comprising a series of dental appliances formoving the patient's teeth.

In any of these methods and systems, the collision detector may berepeatedly (including iteratively) invoked. For example, in any of thesemethods and apparatuses, prior to outputting the one or more treatmentplans, the steps of passing the set of tooth positions for the pluralityof the patient's teeth to the collision detector, measuring themagnitude and velocity of collisions between adjacent teeth and passingthe magnitude and velocity of collisions are repeated for a plurality ofdifferent sets of tooth positions, wherein the treatment plan solvergenerates the different sets of tooth positions.

In any of the methods and systems of generating treatment plansdescribed herein, the treatment plan solver may generate the differentsets of tooth positions while minimizing a numerical function subject toa plurality of numerical limits to get a solution vector including allstages of the one or more orthodontic treatment plans.

Also described herein are methods and apparatuses for rapid review andselection of a treatment plan, in real time, from among a large numberof alternative treatment plans, including plans having differentfeatures, durations and final endpoints for the patient's dentition.Once selected/approved, the chosen treatment plan, including all of thestaging information, may be transmitted for manufacture and delivery tothe dental professional and/or patient. In particular, the methods andapparatuses described herein may permit the presentation of a variety oftreatment plans having different treatment times (e.g., stages) andcosts.

The array of treatment plans may include alternative variations oftreatment plans that are presented to the user (e.g., dentalprofessional, or in some cases, the patient) in parallel, and in realtime. As mentioned, the treatment plan variations may include a varietyof different stages, wherein each stage corresponds to a differentaligner to be worn (e.g., for a predetermined period of time, such asfor a day, a week, two weeks, etc.). The user may display side-by-sideviews, for real-time comparison, of different variations, and/or mayswap between different variations, on a video device (computer, tablet,smartphone, etc.). The display may show the final position of the teethpredicted to result from the treatment and/or it may allow the user toreview all of the different stages (including animations). The user mayuse one or more controls (e.g., buttons, sliders, tabs, etc.), which maybe on the display to toggle between different treatment plans, includingapplying “filters” to show variations with or without a particulardental modification (e.g., interproximal reduction, tooth extraction,aligner attachments, etc.). Alternatively, the controls may be off ofthe display (e.g., on a keyboard, mouse, trackball, etc.).

As used herein, an array of treatment plans may refer to a group oftreatment plans. The array of treatment plans may be unordered orordered, and/or may be part of a single data structure or individualtreatment plans may be maintained in separate data structures.

These methods and apparatus may also allow the user to modify any of thetreatment plans. Many of the modifications made by the user may includevariations of the treatment plans that are already pre-calculated andincluded in the array of treatment plans, thus the modifications may bemade in real time by switching between the different treatment planvariations. The modifications may change one or more properties of thetreatment and therefore the treatment plan. If the modifications gobeyond the variations included in the array of treatment plans, the usermay be notified, and the modified treatment plan may be transmitted backto the remote site for recalculation of the plurality of treatment plans(or the addition of new treatment plans to the array) to incorporatethese changes, and the interactive method of forming and/ormanufacturing the treatment plan may be continued with the new orenlarged array of treatment plan variations including the modificationsrequested by the user.

At the start of any of the methods described herein the dentalprofessional may provide input, including patient-specific preferencesor preferences specific to the dental professional (which may be appliedto all of that dental professionals patients). Such preferences mayinclude tooth movement restrictions (e.g., indicating which teeth shouldnot move as part of the treatment), if interproximal reduction (IPR)should be used, and/or how, when during treatment or where to performIPR, if attachments should be used, where (e.g., on which teeth)attachments should be placed if used, etc. In some variations, themethod or apparatus may need just the name of the dental professional inorder to invoke a predefined set of dental-professional specificpreferences (e.g., looking up the dental professional's predefinedpreferences). The dental professional and/or patient may also specifywhich dental/orthodontic product(s) to use (e.g., which type oforthodontic product to use), which may correspond to properties thateffect treatment, including the number of stages to use, the rate ofmovement of the teeth, etc. As with the dental-professional specificpreferences, the method or apparatus may include a memory storing adatabase (e.g., a look-up table) of properties specific to each dentalproduct.

In any of these methods and apparatuses, another input is typically adigital model of the patient's teeth. The digital model of the patient'steeth, as well as any of the user's patient-specific or user-specificpreferences and/or the dental product(s) to be used may be used asinputs (e.g., sent to a remote site) to generate the array of treatmentplans. The process of generating the treatment plans may be automatedand may be fast (e.g., within a few seconds, minutes, or hours). Eachtreatment plan generated may include a final position, staging (e.g., adescription of tooth movement directions along with a speed associatedwith each stage) and (optionally) a set of aligner features placed oneach tooth to improve predictability of the treatment and ensure teethmovements occur. In generating each of these treatment plans, the finalposition of the teeth may be determined so as to address all or some ofthe patient's clinical conditions (e.g., malocclusions) such a crowding,bite issues, etc., and/or may approximate, as closely as possible, anideal tooth position that may be achieved for the patient's teeth. Eachtreatment plan in the array may be specific to a set of propertiescorrelated with the treatment plan and used to pre-calculate it. Forexample, each treatment plan may be generated using the particular setof treatment properties (“properties”). Properties may refer tomodifications of the patient's teeth. For example, treatment plans maybe pre-calculated for a particular number of stages/time of treatment,for the use or non-use of attachments on the teeth, for the use ofattachment at particular locations, for the use of attachments of aparticular type, for the use or non-use of IPR, for the use of IPR onspecific sub-sets of teeth, for the use of IPR at specific stages, forthe use or non-use of tooth extraction, etc., including all possiblecombinations of these properties. Each of the treatment plans arespecific to the patient and may be independently generated for each setof properties using any of the techniques described herein. Thus, eachtreatment plan may be unique, and may have different tooth positions atany of the different stages and, importantly, may have different finalstages. Although the treatment plans may have some generally similar, ornearly identical, tooth positions for some stages, they are typicallygenerated independently of each other. For this reasons, these treatmentplans may be referred to as partial treatment plans, since the finalposition of the treatment plan, and particularly those in which themaximum number of stages (and therefore the duration of the treatment),may not be the same as a comprehensive treatment plan, which resolvesvirtually all of a patient's orthodontic issues; instead, a partialtreatment plan may partially resolve the orthodontic issues, or mayresolve or partially resolve only some of these orthodontic issues

The collection (e.g., array) of treatment plans may include a matrix ofdifferent treatment plan variations. For example, the various treatmentplans may include variations having different treatment times (e.g.,numbers of stages, corresponding to numbers of aligners in thetreatment), and for each different treatment time, the final positionmay be optimized to address either or both any treatment goals, as wellas approximating as closely as possible an ideal or target finalposition. The array of treatment plans may also include treatment plansthat are variations of each of the plans having different treatmentnumbers, in which one or more particular treatment properties (includingmodifications to the patient's teeth) are included (e.g., with orwithout IPR, with or without extractions, etc.).

Methods and apparatuses described herein may include a display providinga simple interface for treatment planning. The user may modify any ofthe plans with a set of tools provided as controls (buttons, etc.) thatmay be present on the screen or any other input. The user may switchbetween different pre-calculated full treatment plans already in thearray of treatment plans (e.g., by applying filters on/off to showvariations such as with/without IPR, with/without extractions,with/without attachments, which attachments to place on which teeth,which teeth to use IPR, changing spacing distance between teeth,changing leveling strategy from “align by incisal edge” to “align bygingiva margins,” etc.). As mentioned, in some cases, makingmodifications that are not covered by the pre-calculated treatment planvariations in the array of treatment plans may cause the method orapparatus to trigger generating of new treatment plans that replace orare added to the array of existing treatment plans and include the newmodifications. In any of these methods and apparatuses, the treatmentplans may be generated in a manner that ensures manufacturability of theplan as defined by ability to manufacture aligners based on thetreatment plan without human intervention. In additional all of thetreatment plans described herein may be generated so as not to worsenany orthodontic problem (e.g., malocclusion).

For example, described herein are apparatuses (e.g., systems) andmethods for treatment planning that provide interactive treatmentplanning with a user (and/or a subject). In general, the apparatus andmethod may provide multiple, pre-calculated full treatment plans inwhich at least some of plans have different number of stages (e.g.,different time to completion, wherein each stage is an aligner that maybe worn for a predetermined, and continuous, amount of time), and many(if not all) of the treatment plans may have different final toothpositions that address some or all of the treatment goals. The plans maybe annotated to include a description of the treatment plan, which mayindicate the number of stages, the options present/absent, and thetreatment goals met, treatment goals improved, or treatment goals leftas-is. As described herein, these methods and apparatuses may take intoaccount dental professional's preferences in order to maximize thetreatment plans presented. For example the treatment plans that areinitially presented from the array of treatment plans may be selected tohave a higher probability of being acceptable to the dental professional(user), without requiring additional modifications. For example, whengenerating the treatment plans, the user's preferences for treatment ofthe specific patient (which may be based on a questionnaire and/orannotations provided by the user, as will be discussed in greater detailbelow, and/or treatment goals, weights on treatment goals, etc.), and/orgeneral user preferences that may be applied to all of the user'spatients (e.g., standard user practices, etc.) may be used along withthe model of the patient's teeth (and in some variations the product tobe used and/or characteristics of the product to be used) to generatethe collection of treatment plans forming the array. Thus each array maybe custom made for each individual user (e.g., dental professional) andspecific to the patient. In addition, the method and apparatus mayselect which treatment plans to present initially based on predeterminedor set user preferences.

Described herein are methods and apparatuses for the display andselection of multiple treatment plans having different endpoints andnumbers of treatment stages. For example, a method of manufacturing aseries of aligners for a patient's teeth may include: collecting (e.g.,receiving, forming, gathering, downloading, and/or accessing, from aremote site or a local site, and may be collected, for example, in aprocessor to be accessed by the user), an array of treatment plansspecific to the patient's teeth, wherein each treatment plan in thearray describes a set of sequential stages for orthodontic movement ofthe patient's teeth including a final stage, further wherein at leastthree of the treatment plans have different numbers of sequentialstages, and further wherein the array of treatment plans comprises twoor more treatment plans having different treatment properties;displaying on a screen, images of the teeth at the final stage for eachtreatment plan of a subset of the treatment plans from the array oftreatment plans; switching, in real time, between images of the teeth atthe final stages for different treatment plans within the array oftreatment plans based on one or more user-selected controls on thescreen; and transmitting a selected one of the treatment plans forfabrication after the user has chosen the selected one of the treatmentplans displayed on the screen.

The methods and apparatuses described herein may refer to transmittingand receiving to and/or from a remote site, from which the array oftreatment plans specific to the patient's teeth may be generated, theremote site may be remote from the user, and may be accessible via a web(e.g., cloud) server, or the like. In some variations the treatmentplans are generated locally, e.g., on software that is running on theuser's computer/processor, which is the same processor containinginstructions (e.g., code) for executing the interactive treatmentplanning, including receiving the array of treatment plans.

As mentioned, each treatment plan in the array may describe a set ofsequential stages for orthodontic movement of the patient's teethincluding a final stage. The treatment plan may include the finalposition of the patient's teeth, staging for the movements of thepatient's teeth (e.g., a description of tooth movement directions alongwith a speed associated with each stage, which may be key frames,showing relative movement of the teeth over the treatment), and a set ofaligner features placed on each tooth to improve predictability of thetreatment and ensure teeth movements to happen. The treatment plan mayalso include metadata (e.g., annotations) about the number of stages,presence/absence of tooth modifications, effect on the patient'streatment goals, etc.). a

As used herein, the phrase “real time” may refer to the immediate (or aperception of immediate or concurrent) response, for example, a responsethat is within milliseconds so that it is available virtually immediatewhen observed by the user. Near real time may refer to within a fewseconds to a few minutes of concurrent.

The screen used to display and interact with the user may be anyappropriate screen or monitor, including touchscreen and non-touchscreenscreens. The screen may be part of a laptop, desktop, or other computer,including hand-held (e.g., smartphone, tablet, etc.) screens. The screenmay include flat panel displays as well as other displays, includingvirtual reality (e.g., glasses, goggles, etc.) and projections (e.g.,surface projections).

The different treatment properties that may be used to generate thevarious treatment plans may include one or more of: interproximalreduction (IRR)/changing spacing distance between teeth, extraction, andaligner attachments (one or more, at various locations), changingleveling strategy from “align by incisal edge” to “align by gingivamargins,” etc.

As will be described in more detail below, any of the methods describedherein may include generating the plurality of treatment plans, such asgenerating the array of full treatment plans including variations ofdifferent treatment properties. These treatment plans may bepre-calculated. Any number of treatment plans may be included in thearray of treatment plans, typically 3 or more (e.g., 4 or more, 5 ormore, 6 or more, 7 or more, 8 or more, 9 or more, 10 or more, 11 ormore, 12 or more, 13 or more, 14 or more, 15 or more, 16 or more, 17 ormore, 18 or more, 19 or more, 20 or more, 22 or more, 24 or more, 26 ormore, 28 or more, 30 or more, 35 or more, 40 or more, 45 or more, 50 ormore, 55 or more, 60 or more, 65 or more, 70 or more, 80 or more, 90 ormore, 100 or more, 110 or more, 120 or more, etc.). In practice, any ofthese methods may include transmitting a model of the patient's teeth tothe remote site holding the treatment plan generator, which may bereferred to as a treatment plan optimizing engine or treatment planoptimizing generator. The treatment plan generator may be located, e.g.,as part of a processor or other system, at a remote site. Thus, any ofthese methods may include generating, at the remote site, the array oftreatment plans specific to the patient's teeth. The model of thepatient's teeth (upper arch, lower arch, or upper and lower arch) may betransmitted to the remote site and may be received there as a digitalfile or it may be digitized at the remote site. The remote site may be adental laboratory. In addition, the user may transmit a list of toothmovement prescription information (e.g. patient-specific treatmentpreferences), wherein the list of tooth movement prescriptioninformation comprises tooth movement limitations, retractionlimitations, interproximal reduction limitations. In any of thesevariations, the remote site may also receive the users identity and maylook up stored (e.g., in a database) user-specific preferences that maybe applied in any case associated with that user (e.g., user-specifictreatment preferences). The user may also (optionally) transmittreatment details or a reference to a set of treatment details,including product details specific to the one or more types ofdental/orthodontic products to be used, if not included, may be set bydefault. For example, the user may transmit as input to the treatmentplan generator, the name(s) or indicator(s) of particulardental/orthodontic treatment program(s), such as “OrthoGO.” Thetreatment plan generator may then use this name or indicator to look updetails specific to this treatment program from a memory accessible orincluded in the treatment plan generator such as the maximum number ofaligners (e.g., the maximum duration of treatment), etc.

The user may be shown one or, more preferably, multiple treatment plansfor their review (in real time or near real time). In displaying thetreatment plans, the user may be shown the final stage of the treatmentplan (showing the final position of the patient's teeth, as achieved bythe treatment plan), and/or may be shown the metadata about thetreatment plan (e.g., the number of stages, the treated/untreatedcomponents, etc.). Displaying images of the teeth at the final stage foreach treatment plan of the subset of the treatment plans from the arrayof treatment plans may include concurrently displaying images of theteeth at the final stages for treatment plans have different numbers ofsequential stages. The treatment plans may be shown side-by-side forcomparison. In some variations, the user may toggle between “filters” orswitches showing the different treatment plans (e.g., a plan with orwithout IPR, etc.). Because the treatment plans have been pre-calculatedand are in the array, they may be shown in real time, and the user mayeasily switch between different versions, allowing the user to pick anoptimal treatment for the patient.

As mentioned, switching between images of the teeth at the final stagesfor different treatment plans within the array of treatment plans may bebased on one or more user-selected (selectable) controls on the screen,such as switching a treatment plan having a first number of sequentialstages with a treatment plan having the same number of sequential stagesbut having different treatment properties when the user changes one ormore user-selected controls on the screen.

For example, different filters/switches may toggle between treatmentplans showing one or more tooth/treatment modifications. Virtually anymodification may be used, including, for example: one or more of:extractions (of one or more teeth), adjusting of tooth overjet,adjusting for overbites, adjusting for cross bites, interproximalreductions (IPR), including one o or more aligner attachments on theteeth, and anterior to posterior (A-P) correction. These filters maycorrespond to treatment preferences.

The methods and apparatuses described herein may include one or moretools allowing the user to modify one or more of the treatment plans.Tools may be display tools (e.g., allowing rotation, sectioning, etc.)for modifying the display of the tooth shown by the treatment plan(s),or they may modify the treatment plan itself, e.g., modifying theposition and/or orientation of the teeth in the final (or anyintermediate) stage of the treatment plan. Tools may includeadding/removing attachments on the teeth. The tools may include removing(e.g., reducing) material from the side of the tooth/teeth, and/orremoving (e.g., extracting) the teeth.

Any of these methods may include transmitting the modified one or moretreatment plans to the treatment plan optimizing generator (e.g., theremote site where the treatment plan optimizing generator is located) torecalculate the array of treatment plans based on the modifications ofthe one or more treatment plans.

Any of these methods may also allow the user to walk through the entiretreatment plan, either as a key frame display and/or as a more intuitivedisplay of a model (e.g., 3D model or projection) of the user's teeth ineach stage. Thus, any of these methods may include displaying, on thescreen, a plurality of the sequential stages (e.g., images of the teethat each stage) when the user selects a stage selection control. Thesedisplays may be animations, showing movements of the teeth.

Any of the methods and apparatuses describe herein may allow the user toselect a subset of treatment plans from the larger array (set) oftreatment plans. This subset may be used for presentation to a patient,as described below (e.g., in a ‘consulting mode’) or for furthermodification or refinement, including for side-by side comparison. Insome variations, the method or apparatus may automatically select theone or more treatment plans for display to the user, based on predefineduser preferences. For example, any of these methods and apparatuses mayinclude selecting the subset of the treatment plans from the array oftreatment plans to display based on user preferences.

As described above, toggling the display between treatment plans may beperformed by turning on/off one or more “filters” or toggles. Forexample, any of these methods and apparatuses may be configured tofilter one or more of the displayed images of the teeth at the finalstage of the subset of the treatment plans from the array of treatmentplans when the user selects a filter control.

For example, a method of manufacturing a series of aligners for apatient's teeth may include: transmitting a model of the patient's teethto a remote site; transmitting a list of tooth movement prescriptioninformation to the remote site; collecting (e.g., receiving, gathering,downloading, and/or accessing) from the remote site, an array oftreatment plans specific to the patient's teeth, wherein each treatmentplan in the array describes a set of sequential stages for orthodonticmovement of the patient's teeth having a final stage, further wherein atleast three of the treatment plans have different numbers of sequentialstages, and further wherein, for each number of sequential stages, thearray comprises two or more treatment plans having the same number ofsequential stages but treatment properties; displaying on a screen,images of the teeth at the final stage for each treatment plan of asubset of the treatment plans from the array of treatment plans;switching, in real time, between images of the teeth at the final stagesfor different treatment plans within the array of treatment plans basedon one or more user-selected controls on the screen; and transmitting aselected one of the treatment plans for fabrication after the user haschosen the selected one of the treatment plans displayed on the screen.

Any of the methods described herein may be performed by an apparatusconfigured to perform the method steps. In particular, described hereinare apparatuses (e.g., systems) that are configured to executeinstructions (code) to control an apparatus having a processor, display,input, etc. to interactively allow a user to design and manufacture aseries of aligners for correction of malocclusions of a patient's teeth.Any of these apparatuses may be configured as non-transient,computer-readable media (e.g., software, firmware, hardware or somecombination thereof) that includes instructions for controlling theapparatus as described herein and may be part of a system or sub-system.

For example, described herein are non-transient, computer-readable mediacontaining program instructions for causing a computer to: receive, froma remote site, an array of treatment plans specific to the patient'steeth, wherein each treatment plan in the array describes a set ofsequential stages for orthodontic movement of the patient's teethincluding a final stage, further wherein at least three of the treatmentplans have different numbers of sequential stages, and further whereinthe array of treatment plans comprises two or more treatment planshaving different treatment properties; display on a screen, images ofthe teeth at the final stage for each treatment plan of a subset of thetreatment plans from the array of treatment plans; switch, in real time,between images of the teeth at the final stages for different treatmentplans within the array of treatment plans based on one or moreuser-selected controls on the screen; and transmit a selected one of thetreatment plans for fabrication after the user has chosen the selectedone of the treatment plans displayed on the screen. Also describedherein are systems including one or more processors configured toexecute the program instructions. These systems may be referred toherein as treatment plan comparators (or interactive, real-timetreatment plan comparators), and may optionally or additionally includeone or more displays, one or more user selectable controls and one ormore communications circuitry (e.g., a communications module, such as awireless circuit, etc.).

The different treatment properties that may be varied between thedifferent treatment plans may include treatment preferences, such as oneor more of: allowing or restriction interproximal reduction (IRR),allowing or restriction extraction, and allowing or restricting alignerattachments (e.g., attachments on the teeth to couple to the aligner).The program instructions may be further configured to transmit a modelof the patient's teeth to the remote site. The program instructions maybe further configured to, generate at the remote site, the array oftreatment plans specific to the patient's teeth.

The program instructions may be configured to transmit a list of toothmovement prescription information (e.g., to the remote site containingthe treatment plan optimizing generator), wherein the list of toothmovement prescription information may include tooth movementlimitations, retraction limitations, interproximal reductionlimitations.

The program instructions may be configured to display images of theteeth at the final stage for each treatment plan of the subset of thetreatment plans from the array of treatment plans by concurrentlydisplaying images of the teeth at the final stages for treatment planshave different numbers of sequential stages.

The program instructions may be configured to switch between images ofthe teeth at the final stages for different treatment plans within thearray of treatment plans based on one or more user-selected controls onthe screen by switching a treatment plan having a first number ofsequential stages with a treatment plan having the same number ofsequential stages but having different treatment properties based on oneor more user-selected controls on the screen. The different treatmentproperties may include one or more of: extractions, overjets, overbites,cross bites, interproximal reductions, attachments, and anterior toposterior (A-P) correction. The program instructions may be furtherconfigured to provide one or more tools allowing the user to modify oneor more of the treatment plans.

The program instructions may be further configured to transmit themodified one or more treatment plans to the remote site to recalculatethe array of treatment plans based on the modifications of the one ormore treatment plans. The program instructions may be further configuredto display, on the screen, a plurality of the sequential stages when theuser selects a stage selection control. The stage selection control mayallow the user to dynamically, in real time, view the different stages(e.g., positions of the teeth in each stage).

The program instructions may be further configured to select the subsetof the treatment plans from the array of treatment plans to displaybased on user preferences. The program instructions may be furtherconfigured to filter one or more of the displayed images of the teeth atthe final stage of the subset of the treatment plans from the array oftreatment plans when the user selects a filter control.

As mentioned, any of these methods and apparatuses may include aconsultation mode that presents multiple treatment plans to the patientor physician, including treatment plans having different numbers ofstages and different final tooth positions. These displayed treatmentplans may be selected by the user (e.g., dental professional) as asubset of the treatment plans in the array. The displayed treatmentplans (and any corresponding metadata about them) may be displayedsequentially or simultaneously (e.g., side-by-side) for viewing by thepatient. Pricing information may also be shown corresponding to eachtreatment plan, along with a graphical display that allows the patient(and/or user) to see the final tooth positions and allows the user toselect the desired outcome. Multiple treatment plans having a differentnumber of stages and different final tooth positions may be presented tothe patient, and the patient (by themselves or in consultation with thedental professional) may decide which treatment plan to select.

Once a treatment plan is selected, it may be used to generate a seriesof aligners. For example, the treatment plan may be transmitted to amanufacturing facility that may directly print (e.g., by 3D printing)each aligner in the series, or the treatment plan may be used togenerate a positive model of the patient's teeth at each stage used forforming the aligners (e.g., by thermoforming).

Thus, in consultation mode the patient is presented with multipletreatment plans having different numbers of stages and allowed to selectwhich treatment plan to manufacture and use.

For example, a method of manufacturing a series of aligners for apatient's teeth may include a consultation mode. For example, the methodmay include: collecting (e.g., receiving, forming, gathering,downloading, and/or accessing), in a processor, an array of treatmentplans specific to the patient's teeth, wherein each treatment plan inthe array describes a set of sequential stages for orthodontic movementof the patient's teeth, including a final stage, further wherein atleast three of the treatment plans have different numbers of sequentialstages, and further wherein the final stages of the treatment planswithin the array of treatment plans are different; displaying, on ascreen, images of the teeth at the final stages for a subset of thetreatment plans from the array of treatment plans; selecting, by a user,two or more treatment plans from the subset of the treatment plans usingone or more controls on the screen; and displaying, to the patient, thetwo or more treatment plans from the subset of the treatment plans; andtransmitting a selected one of the two or more treatment plans forfabrication after the patient has chosen the selected one of thetreatment plans.

As mentioned, any of these method may include transmitting a model ofthe patient's teeth to a remote site (e.g., the location of thetreatment plan optimizing generator). Displaying the two or moretreatment plans may include displaying annotations describing changes inthe final stage of each of the two or more treatment plans compared tothe model of the patient's teeth. The annotations (which may be“metadata” about the treatment plan) may comprise one or more of:changes in the malocclusion, changes in the patient's bite, and changesin the upper and/or lower crowding.

Displaying, to the patient, the two or more treatment plans from thesubset of the treatment plans may comprise displaying the number ofsequential stages.

Any of these methods may include switching, in real time, one or more ofthe images of the teeth at the final stages of the subset for differenttreatment plans with an image of the final stage of one or more othertreatment plans from the array of treatment plans, based on one or moreuser-selected controls on the screen. The two or more treatment plansfrom the subset of the treatment plans may comprise two or moretreatment plans having different numbers of sequential stages.

For example, a method of manufacturing a series of aligners for apatient's teeth may include: transmitting a model of the patient's teethto a remote site; collecting (e.g., receiving, forming, gathering,downloading, and/or accessing), from the remote site, an array oftreatment plans specific to the patient's teeth, wherein each treatmentplan in the array describes a set of sequential stages for orthodonticmovement of the patient's teeth, including a final stage, furtherwherein at least three of the treatment plans have different numbers ofsequential stages, and further wherein the final stages of the treatmentplans within the array of treatment plans are different; displaying, ona screen, images of the teeth at the final stages for a first subset ofthe treatment plans from the array of treatment plans; selecting, by auser, two or more treatment plans from the first subset of the treatmentplans using one or more controls on the screen; displaying, to thepatient, the two or more treatment plans and annotations describingchanges in the final stage of each of the two or more treatment planscompared to the model of the patient's teeth; and transmitting aselected one of the two or more treatment plans for fabrication afterthe patient has chosen the selected one of the treatment plans.

Also described herein are non-transient, computer-readable mediumcontaining program instructions for causing a computer to: receive, in aprocessor, an array of treatment plans specific to the patient's teeth,wherein each treatment plan in the array describes a set of sequentialstages for orthodontic movement of the patient's teeth, including afinal stage, further wherein at least three of the treatment plans havedifferent numbers of sequential stages, and further wherein the finalstages of the treatment plans within the array of treatment plans aredifferent; display, on a screen, images of the teeth at the final stagesfor a first subset of the treatment plans from the array of treatmentplans; select, by a user, two or more treatment plans from the firstsubject of the treatment plans using one or more controls on the screen;and display, to the patient, the two or more treatment plans; andtransmit a selected one of the two or more treatment plans forfabrication after the patient has chosen the selected one of thetreatment plans.

In general, the methods and apparatuses described herein provideinteractive treatment planning, and may present multiple, full andpre-calculated treatment plans to a user (e.g., dental professional) andallows the user to switch between views of different pre-calculatedtreatment plans, and to modify the one or more treatment plans. Thesystems and methods described herein may also allow for the doctor tochange final position and re-calculate a new final position real timewithout sending it to the technician

Also described herein are methods and apparatuses (e.g., non-transient,computer-readable medium containing program instructions for causing acomputer to perform steps) for creating one or more (e.g., an array of)treatment plans to align, including partially aligning, a patient'steeth.

For example, described herein are automated methods of creating atreatment plan to align a patient's teeth using a plurality of removablealigners to be worn in sequential stages, the method comprising:collecting (e.g., receiving, forming, gathering, downloading, and/oraccessing), in a processor: a digital model of a patient's teeth, a setof treatment preferences and/or a reference to a set of treatmentpreferences, a comprehensive final position of the patient's teeth, and(optionally) a set of treatment details or an identifier identifying theset of treatment details; selecting a plurality of numerically expressedtreatment targets and constraints from a memory accessible to theprocessor, based on the set of treatment details, the set of treatmentpreferences and the comprehensive final position of the patient's teeth;combining the plurality of numerically expressed treatment targets toform a single numerical merit function; selecting a plurality of numericlimits on the treatment constraint functions based on the set oftreatment details, the set of treatment preferences and thecomprehensive final position of the patient's teeth; minimizing thesingle numerical merit function to get a solution vector including allstages forming the treatment plan, subject to the plurality of limits onnumeric treatment constraints; and mapping the solution vector to atreatment plan, wherein the treatment plan includes a final toothposition that is different from the comprehensive final position of thepatient's teeth.

In general, treatment details may refer to a product definition, whichmay be the parameters set by the properties of the aligner product to beused for the treatment, e.g., the number of stages, the rate of toothmovement, etc. Treatment preferences may refer to the treatmentpreferences of the dental practitioner (e.g., which teeth not to move,etc.) and may be specific to the patient, or may be specific to the userand applied to all of the user's patient's. Thus, treatment details mayinclude details about the product(s) that may be used to achieve thetreatment, including the number and type of aligners, and any propertiesof the aligners themselves. In some variations, the treatment detailsare not provided separately to the method or apparatus, but areavailable (e.g., as a default) when generating the one or more treatmentplans. The method or apparatus may default to a single set of treatmentdetails, corresponding to a single dental/orthodontic product, or it maybe selected from a listing of predefined products having specifiedproperties. Alternatively, the user may provide the details specific toa particular product or products, forming the treatment details. Notethat when a plurality of different treatment plans are to be generated,forming an array of treatment plans, the various sets of treatmentdetails, corresponding to different dental/orthodontic products, may beused to generate different variations.

Examples of treatment preferences are described in detail herein. Forexample, treatment preferences may include one or more of: an indicatorof which teeth are not permitted to move, an indication of which teethshould not have an attachment, an indicator of which teeth to treat, anindicator of tooth class correction amount, an indicator thatinterproximal reduction is to be used, an indicator that arch expansionis to be used, and indicator of spacing between teeth, an indicator ortooth levelling. The identifier identifying the treatment details mayidentify a product having a defined set of treatment details accessibleto the processor.

Examples of treatment details (corresponding to the properties ofdifferent products that may be used) are also provided below, but mayinclude one or more of: a maximum allowed number of stages, whetherattachments to the patient's teeth are allowed, a maximum allowed toothroot movement, a maximum allowed tooth crown movement, and a maximumallowed tooth rotation.

Combining the numerically expressed treatment targets may mean weightingeach of the numerically expressed treatment targets in the singlenumerical function. A weight factor may be used to multiple any of thenumerically expressed treatment targets; different weight factors may beused for each or a subset of the numerically expressed treatmenttargets. Weighting factors may be set empirically or may be adjusted bythe apparatus.

The single numerical function may include, for a set of teeth, a sum ofat least: a difference from the positions of the teeth compared to thecomprehensive final position of the patient's teeth, a measure ofmisalignment in an x direction for the teeth, a measure of misalignmentin a z direction for the teeth, a measure of misalignment of a dentalarch of the teeth, a measure of diastema between neighboring teeth, ameasure of overjet of the teeth, a measure of overbite of the teeth, ameasure of collisions between the teeth, a measure of the differencebetween an arch of the teeth and the comprehensive final position of thepatient's teeth, a measure of the difference in leveling between theteeth and the comprehensive final position of the patient's teeth, ameasure of the amount of occlusion between the teeth of the patient'supper and lower jaws, a measure of the difference in the amount ofocclusion between the teeth and the comprehensive final position of thepatient's teeth, a measure of the amount of mesial to distal round tripsof the teeth, a measure of the amount of buccal to lingual round tripsof the teeth, and a measure of a number of aligner stages compared to atarget number of aligner stages from the set of treatment details. Forexample, the single numerical function may include, for a set of teeth,a sum of at least: a difference from the positions of the teeth comparedto the comprehensive final position of the patient's teeth, a measure ofmisalignment for the teeth, and a measure of a number of aligner stagescompared to a target number of aligner stages from the set of treatmentdetails.

The methods described herein may also include adjusting the plurality ofnumerically expressed treatment targets into a plurality of adjustednumerically expressed treatment targets based on: the set of treatmentdetails, the set of treatment preferences and the comprehensive finalposition of the patient's teeth, further wherein combining the pluralityof numerically expressed treatment targets comprises combining theplurality of adjusted numerically expressed treatment targets.

The plurality of numeric limits may comprise one or more of: a maximumvelocity of tooth movement, a maximum amount of collision between teeth,a tooth movement limitation, a maximum number of aligner stages, amaximum amount of occlusion, a maximum amount of occlusion, a maximumamount of overbite, a maximum amount of overjet, and a maximum midlineposition.

In general, minimizing the single numerical function subject to theplurality of numeric limits may comprise using a constrainedoptimization method to get a solution vector. The constrainedoptimization method may comprise an interior point method (e.g.,interior point method variations such as SQP and Active Set).

Mapping the solution vector to a treatment plan may comprises convertingthe solution vector into a set of key frames for each tooth,corresponding to a stage number, and positional information for eachtooth, including an x coordinate, a y coordinate, a z coordinate, and anangulation, an inclination and a rotation angle. In mapping the solutionvector to form a key function, the solution vector may include numerouskey function components that may be combined to form the complete keyfunction set for the treatment plan. Thus, mapping the solution vectorto a treatment plan may include, for some teeth, mapping a singlevariable in the solution vector to a single coordinate or angle in a keyframe, while for some teeth, mapping may include mapping a linearcombination of multiple variables from the solution vector to a singlecoordinate or angle in a key frame.

The method may also include displaying the final tooth position of thetreatment plan and/or transmitting the treatment plan to be displayed.

For example, an automated method of creating a treatment plan to align apatient's teeth using a plurality of removable aligners to be worn insequential stages, may include: collecting (e.g., receiving, forming,gathering, downloading, and/or accessing), in a processor: a digitalmodel of a patient's teeth; accessing (by the processor) a set oftreatment preferences, a comprehensive final position of the patient'steeth, and a set of treatment details; selecting a plurality ofnumerically expressed treatment targets from a memory accessible to theprocessor based on: the set of treatment details, the set of treatmentpreferences and the comprehensive final position of the patient's teeth;adjusting the plurality of numerically expressed treatment targets intoa plurality of adjusted numerically expressed treatment targets basedon: the set of treatment details, the set of treatment preferences andthe comprehensive final position of the patient's teeth; combining theplurality of adjusted numerically expressed treatment targets to form asingle numerical function; setting a plurality of numeric limits on thesingle numerical function based on the set treatment preferences;minimizing (e.g., iteratively) the single numerical function subject tothe plurality of numeric limits to get a solution vector including allstages forming the treatment plan; and mapping the solution vector to atreatment plan, wherein the treatment plan includes a final toothposition that is different from the comprehensive final position of thepatient's teeth.

Accessing the set of treatment preferences may include collecting (e.g.,receiving, forming, gathering, downloading, and/or accessing in theprocessor) the set of treatment preferences, or collecting a referenceto a set of treatment preferences that the processor may use to look upa set of (e.g. one or more) treatment preferences from a memoryaccessible by the processor holding, for example, a look-up table ofpreferences indexed by a reference. Accessing the comprehensive finalposition of the patient's teeth may include receiving the comprehensivefinal position (e.g., as a digital model or representation of positionsof the patient's teeth), or it may include generating, using theprocessor, the comprehensive final position. The comprehensive finalposition may be manually or semi-manually generated and a digital copysent to the processor. If the processor has already generated thecomprehensive final position, the processor may store it in a memory andaccess it later (e.g., during additional cycles). Accessing the set oftreatment details may include accessing a stored (in a memory) set oftreatment details, including accessing a ‘default’ set of treatmentdetails, receiving the set of treatment details, or it may includereceiving an identifier identifying the set of treatment details andusing the identifier to look up, from a memory (e.g. holding a look-uptable) a set of treatment details. The identifier may be a productname/model, etc.

Also described herein are apparatuses for performing any of thesemethods as a non-transient, computer-readable medium containing programinstructions for creating a treatment plan to align a patient's teethusing a plurality of removable aligners. For example, the programinstructions may cause a processor to: receive, in the processor: adigital model of a patient's teeth, a set of treatment preferences or areference to a set of treatment preferences, a comprehensive finalposition of the patient's teeth, and a set of treatment details or anidentifier identifying the set of treatment details; select a pluralityof numerically expressed treatment targets from a memory accessible tothe processor, based on the set of treatment details, the set oftreatment preferences and the comprehensive final position of thepatient's teeth; combine the plurality of numerically expressedtreatment targets to form a single numerical function; select aplurality of numeric limits on the single numerical function based onthe set treatment preferences; minimize the single numerical functionsubject to the plurality of numeric limits to get a solution vectorincluding all stages forming the treatment plan; and map the solutionvector to a treatment plan, wherein the treatment plan includes a finaltooth position that is different from the comprehensive final positionof the patient's teeth.

As mentioned above, the treatment preferences may comprise one or moreof: an indicator of which teeth are not permitted to move, an indicationof which teeth should not have an attachment, an indicator of whichteeth to treat, an indicator of tooth class correction amount, anindicator that interproximal reduction is to be used, an indicator thatarch expansion is to be used, and indicator of spacing between teeth, anindicator or tooth levelling. The identifier identifying the treatmentdetails may identify a product having a defined set of treatment detailsaccessible to the processor.

The set of treatment details may comprises one or more of: a maximumallowed number of stages, whether attachments to the patient's teeth areallowed, a maximum allowed tooth root movement, a maximum allowed toothcrown movement, and a maximum allowed tooth rotation. Combining thenumerically expressed treatment targets may further comprise weightingeach of the numerically expressed treatment targets in the singlenumerical function.

The single numerical function may include, for a set of teeth, a sum ofat least: a difference from the positions of the teeth compared to thecomprehensive final position of the patient's teeth, a measure ofmisalignment in an x direction for the teeth, a measure of misalignmentin a z direction for the teeth, a measure of misalignment of a dentalarch of the teeth, a measure of diastema between neighboring teeth, ameasure of overjet of the teeth, a measure of overbite of the teeth, ameasure of collisions between the teeth, a measure of the differencebetween an arch of the teeth and the comprehensive final position of thepatient's teeth, a measure of the difference in leveling between theteeth and the comprehensive final position of the patient's teeth, ameasure of the amount of occlusion between the teeth of the patient'supper and lower jaws, a measure of the difference in the amount ofocclusion between the teeth and the comprehensive final position of thepatient's teeth, a measure of the amount of mesial to distal round tripsof the teeth, a measure of the amount of buccal to lingual round tripsof the teeth, and a measure of a number of aligner stages compared to atarget number of aligner stages from the set of treatment details.

The non-transient, computer-readable medium of claim 15, wherein thesingle numerical function includes, for a set of teeth, a sum of atleast: a difference from the positions of the teeth compared to thecomprehensive final position of the patient's teeth, a measure ofmisalignment for the teeth, and a measure of a number of aligner stagescompared to a target number of aligner stages from the set of treatmentdetails.

The program instructions may be further configured to adjust theplurality of numerically expressed treatment targets into a plurality ofadjusted numerically expressed treatment targets based on: the set oftreatment details, the set of treatment preferences and thecomprehensive final position of the patient's teeth. Further, theprogram instructions may also be configured to combine the plurality ofnumerically expressed treatment targets by combining the plurality ofadjusted numerically expressed treatment targets.

The plurality of numeric limits may comprise one or more of: a maximumvelocity of tooth movement, a maximum amount of collision between teeth,a tooth movement limitation, a maximum number of aligner stages, amaximum amount of occlusion, a maximum amount of occlusion, a maximumamount of overbite, a maximum amount of overjet, and a maximum midlineposition. The program instructions may be further configured to minimizethe single numerical function subject to the plurality of numeric limitsusing a constrained optimization method to get a solution vector.

The program instructions may be further configured to map the solutionvector to a treatment plan by converting the solution vector into a setof key frames for each tooth, corresponding to a stage number, andpositional information for each tooth, including an x coordinate, a ycoordinate, a z coordinate, and an angulation, an inclination and arotation angle.

The program instructions may be configured to provide the final toothposition of the treatment plan for display.

Any of the methods and apparatuses described herein may be configured togenerate an array of treatment plan variations. This may be achieved,for example, by modifying, either automatically or manually, thetreatment preferences and/or treatment details. For example, the maximumnumber of stages (corresponding to the number of aligners to be used ina treatment) may be modified to generate treatment plan variationshaving different treatment durations, since the duration of treatment istypically correlated to the number of aligners to be worn. Although ingeneral, the more stages/aligners used, the greater the overall amountof correction that may be achieved, as described herein (e.g.,approaching a comprehensive final position of the teeth which may beconsidered an optimal treatment plan) in some cases it may be preferableby the patient and/or dental professional to limit the duration oftreatment and settle for an improved, but not perfectly corrected,alignment.

Also described herein are methods of modifying a treatment plan for aseries of aligners and/or manufacturing a series of aligners for apatient's teeth. For example a method may include: transmitting a modelof the patient's teeth to a remote site; transmitting a list of toothmovement prescription information to the remote site; collecting aplurality of treatment plans specific to the patient's teeth using anideal final position for the patient's teeth and the model of thepatient's teeth, wherein each treatment plan in the plurality oftreatment plans describes a set of sequential stages for orthodonticmovement of the patient's teeth having a final stage, further wherein,for each treatment plan the final stage is different from the idealfinal position for each of the different treatment properties of thepatient's teeth; ranking the plurality of treatment plans based on howcomprehensive they are compared to the ideal final position; anddisplaying on a screen, images of the patient's teeth at the final stagefor either the first or the first and second treatment plans from thearray of treatment plans; switching, in real time, between images of theteeth at the final stages for different treatment plans within the arrayof treatment plans based on one or more user-selected controls on thescreen; and transmitting a selected one of the treatment plans forfabrication after the user has chosen the selected one of the treatmentplans displayed on the screen.

The different treatment properties may comprise one or more of:interproximal reduction (IRR), extraction, and aligner attachments. Forexample, the tooth movement prescription information may comprise toothmovement limitations, retraction limitations, interproximal reductionlimitations.

Any of these methods may include switching between images of the teethat the final stages for different treatment plans within the array oftreatment plans based on one or more user-selected controls on thescreen by switching a treatment plan having a first number of sequentialstages with a treatment plan having the same number of sequential stagesbut having different treatment properties based on one or moreuser-selected controls on the screen.

Ranking based on how comprehensive the treatment plan is may includelooking up a score from a database of rankings indexed by two or moreof: interproximal reductions, attachments, dental aligner product,extractions, overjets, overbites, cross bites, and anterior to posterior(A-P) correction. Alternatively or additionally, ranking based on howcomprehensive the treatment plan is may include scoring the treatmentplan based on three or more of: interproximal reductions, attachments,dental aligner product, extractions, overjets, overbites, cross bites,and anterior to posterior (A-P) correction.

The method may also include modifying one or more of the treatment plansusing the user interface and transmitting the modified one or moretreatment plans to the remote site to recalculate the array of treatmentplans based on the modifications of the one or more treatment plans.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of the invention are set forth with particularity inthe claims that follow. A better understanding of the features andadvantages of the present invention will be obtained by reference to thefollowing detailed description that sets forth illustrative embodiments,in which the principles of the invention are utilized, and theaccompanying drawings of which:

FIG. 1A is a tooth repositioning appliance, shown in this example as analigner or shell aligner.

FIG. 1B illustrates a series of tooth repositioning appliances(aligners) configured to be worn sequentially (over the course ofmultiple days or weeks) for repositioning a patient's teeth.

FIG. 2A is a schematic example of a treatment plan solver (e.g., anautomated orthodontic treatment planning system).

FIG. 2B is a schematic example of a collision detector (e.g., anautomated collision detection system).

FIG. 2C schematically illustrates one example of an automated method ofcreating one or more treatment plans to align a patient's teeth (e.g.,using a series of removal aligners to be worn in a sequence).

FIG. 2D schematically illustrates one example of an automatic collisiondetection method that may be used, e.g., by the treatment plan solverperforming an automated treatment planning method. The illustratedautomatic collision detection method may be performed, for example, by acollision detector.

FIG. 3 illustrates an example of a method for manufacturing a series ofaligners for a patient's teeth in which a plurality of treatment plansspecific to the patient's teeth, representing partial treatment plans,having a fixed number of different stages and variations of these fixednumber stages are all pre-calculated and included and displayed inreal-time to allow the user to interactively select and/or modify atreatment plan for an orthodontic treatment. The method of manufacturingthe series of aligners may include an automated method of creating oneor more treatment plans or a treatment plan solver configured to performthe automated method of creating one or more treatment plans and/or anautomatic collision detection method or a collision detector configuredto perform an automatic collision detection method.

FIG. 4 is an illustration of a method for consulting with a patient byinteractively showing them a subset of the treatment plans (e.g.,selected by the user).

FIG. 5 is an example of a detailed process chart for designing,selecting and/or modifying a treatment plan and for manufacturing theselected treatment plan.

FIG. 6 is another example of a detailed process chart for designing,selecting and/or modifying a treatment plan and for manufacturing theselected treatment plan.

FIG. 7A is an example of a display for simultaneously showing, in realtime, multiple treatment plans, including filters for toggling betweentreatment plans that are variations of fixed-length (e.g., “partial”)treatment plans having a preset/predetermined number of stages.

FIG. 7B is another example of a display for simultaneously showing, inreal time, multiple treatment plans.

FIG. 7C is a schematic example of an interactive real-time treatmentplan comparator.

FIG. 7D schematically illustrates one example of a method forinteractive real-time treatment plan comparison, which may be part of amethod of manufacturing a series of aligners for a patient's teeth.

FIG. 8A is a user interface for a user (e.g., clinician, orthodontist,dentist, etc.) that may be executed as a non-transient,computer-readable medium containing program instructions for causing acomputer to execute control to interactively display, select and/ormodify treatment plans.

FIG. 8B is another example of a user interface, configured as aninteractive prescription interface.

FIG. 9A is an example of a user interface showing the concurrent,real-time, display of multiple treatment plans showing treatments fixedat 26, 14 and 7 stages, respectively. In FIG. 9A, the final toothconfiguration achieved by each treatment plan is shown for comparison,and toggles (filter controls) are included for showing alterativetreatment plans calculated with/without IPR and with/withoutattachments. Additional filters may be included.

FIG. 9B shows the user interface of FIG. 9A after selecting (turning on)two filters, so that the treatment plan on the right (fixed at 26stages) is a treatment plan including both IPR and attachments, andresults in resolution of the patient's crowding treatment target andpartially resolves the patient's open bite.

FIGS. 9C, 9D and 9E are examples of user interfaces that interactivelydisplays and allows the user to modify (and resubmit) one or moretreatment plans. FIG. 9C is an example of a user interface showing aninteractive treatment planning screen in which a model (3D digitalmodel) of the patient's dentition is included in a large display window.FIG. 9D is an example of a user interface that includes a window forshowing one or both of the patient's dental arches at any stage of aproposed treatment plan. FIG. 9E is another example of a user interface,similar to that shown in FIG. 9D.

FIG. 9F is an example of a user interface configured for side-by-sidecomparison of one or more variables that may be considered whengenerating multiple treatment plans.

FIG. 9G is an example of a user interface configured to show ‘before’and ‘after’ images of the patient's dentition, wherein the beforetreatment image is shown on the left, while the proposed/predictedoutcome of a specified treatment plan is shown on the right.

FIG. 9H is an example of a patient presentation user interface that maybe provided to the patient to illustrate the predicted outcome of thetreatment, and/or to allow a comparison between different treatmentplans.

FIG. 10A shows a user interface (display) in which a 26 stage treatmentplan including both IPR and aligner attachments is shown; controls onthe screen (e.g., slider) allow the user to view the predicted toothposition in each stage.

FIG. 10B shows the user interface (display) of FIG. 10A, including theadjustments for spacing (shown by the + symbols) and/or leveling. Othertools may be included for modifying the treatment plan.

FIG. 10C is a user interface confirming submission of the modifiedtreatment plan for recalculation of one or more treatment plans (whichmay be added to the array for further display, selection and/ormodification).

FIG. 11A is another example of a user interface such as the one shown inFIG. 10A, in which the user may comment (e.g., via text) for additionalmodifications.

FIG. 11B is a user interface confirming submission of the modifiedtreatment plan for recalculation of one or more treatment plans (whichmay be added to the array for further display, selection and/ormodification).

FIG. 12 is an example of a user interface configured as a consultationsummary screen for use in a consultation mode to display a subset of thetreatment plans to a subject (e.g., patient) to allow them to selectbetween treatment options. In FIG. 12 12, the patient (Joe Smith) isbeing shown two options, a treatment plan having 26 stages with IPR andaligner attachments, and a second treatment plan having 14 stageswithout either IPR or aligners. The user interface (display) alsoindicates that the 26 stage treatment plan resolves the therapeutic goalof reducing crowding and open bite; the 14 stage treatment plan resolvesthe crowding (but not the open bite). The user interface also indicatesthe treatment goals upper and lower crowding and open bite) as themalocclusion analysis.

FIG. 13 is another example of a user interface configured forconsultation with the patient. In FIG. 13, the user interface shows thepatient's current dentition (“now”) and identifies two malocclusionissues, and shows a 26 stage treatment plan (center) and a 14 stagetreatment plan (right). The 26 stage treatment plan resolves the upperand low crowding and the open bite. The 14 stage treatment plan resolvesthe upper and lower crowding and partially resolves the open bite.

FIG. 14 is an example of a user interface showing a 3D model of thepatient's teeth as they are moved during an exemplary 26 stage treatmentplan. The display includes a control allowing the user to animate thedisplay (moving from the initial, untreated condition, to the finalposition, or manually selecting any of the treatment stages.

FIG. 15 illustrates a display showing progression of a patient'smalocclusion over time (from 2005 to 2011). The user interface may allowthe user to select and display image form the patient's dental record inaddition to one or more treatment plans from the array of treatmentplans.

FIG. 16A is a frontal view of a digital model (e.g., scan) of apatient's dental arch, in an untreated configuration.

FIGS. 16B-16M graphically illustrates an array of treatment plans,showing the final stage positions of the patient's teeth for each of 12treatment plans. FIGS. 16B, 16C and 16D show the final stage toothpositions of a treatment plans generated assuming that no alignerattachments would be used, and no IPR is used on the patient's teeth; inFIG. 16B the treatment was limited to 26 stages, in FIG. 16C thetreatment plan is limited to 14 stages and in FIG. 16D the treatmentplan is limited to 7 stages. FIGS. 16E, 16F and 16G show the final stagetooth positions of a treatment plans generated assuming that alignerattachments would be used, and no IPR will be performed on the patient'steeth; in FIG. 16E the treatment was limited to 26 stages, in FIG. 16Fthe treatment plan is limited to 14 stages and in FIG. 16G the treatmentplan is limited to 7 stages. FIGS. 16H, 16I and 16J show the final stagetooth positions of a treatment plans generated assuming that no alignerattachments would be used, but that IPR will be performed on thepatient's teeth; in FIG. 16H the treatment was limited to 26 stages, inFIG. 16I the treatment plan is limited to 14 stages and in FIG. 16J thetreatment plan is limited to 7 stages.

FIGS. 16K, 16L and 16M show the final stage tooth positions of atreatment plans generated assuming that aligner attachments would beused, and IPR will be performed on the patient's teeth; in FIG. 16K thetreatment was limited to 26 stages, in FIG. 16L the treatment plan islimited to 14 stages and in FIG. 16M the treatment plan is limited to 7stages.

FIG. 17 is another example of a user interface illustrating thereal-time display of multiple treatment plans having limited numbers ofstages. In FIG. 17 the left panel shows the final position of the teethfollowing a treatment plan that was generated by limiting the number ofstages to 26 stages. The user controls on the right of the userinterface (“filters”) may be used to select one or more differenttreatment plans including a different number of stages (“product”),different treatment properties (e.g., IPR, attachments). The userinterface may also show preferences (“apply template”) and may show anyof these variations in real time, by immediately switching between thedifferent treatment plans. The control on the bottom of the left panelallows the user to select and display the teeth position of any of thestages. As in any of the user interfaces, the currently displayedtreatment plan may be selected for comparison as part of a consultationscreen. Additional controls may allow modification of the treatmentplan(s) or immediate manufacturing/ordering of a series of alignerscorresponding to the selected treatment plan.

FIG. 18 illustrates a sequence of a linear treatment planning methodusing a comprehensive final position as the final position of theplanned treatment.

FIG. 19 is a graphically illustration of a method for automaticallygenerating optimized treatment plans described herein.

FIG. 20A illustrates a sequence of an optimization-based partialtreatment planning method (e.g., an automated method of creating atreatment plan to align a patient's teeth using a plurality of removablealigners to be worn in sequential stages) as described herein.

FIG. 20B is another schematic illustration of a method of creating atreatment plan to align a patient's teeth using a plurality of removablealigners to be worn in sequential stages.

FIG. 20C is an alternative illustration of a method of creating atreatment plan to align a patient's teeth using a plurality of removablealigners to be worn in sequential stages.

FIG. 21 illustrates the use of a non-linear constrained optimizationmethod to generate a treatment plan.

FIG. 22A illustrates one method of quantifying occlusion between upperand lower jaw so that it may be expressed as a numeric expression.

FIGS. 22B-22D show patient cross bite correction from a startingposition (FIG. 22A) using a full treatment plan (FIG. 22C), and partial,optimized treatment plan (FIG. 22D).

FIG. 23 shows quantification of x-misalignment so that it may beexpressed as a numeric expression.

FIG. 24 illustrates quantification of z-misalignment so that it may beexpressed as a numeric expression.

FIG. 25 shows alignment to arch quantification so that it may beexpressed as a numeric expression.

FIGS. 26A-26B illustrate annotation of tooth movement showing atrajectory with four key frames.

FIG. 27 illustrates one method of generating treatment preferences(e.g., user-specific/dental professional specific treatment preferences)that may be used to automatically generate a treatment plan or set oftreatment plans.

FIG. 28 shows another example of a method of generating a treatment planin which the treatment plan generator (engine) accesses a set ofuser-specific treatment preferences.

FIG. 29A shows an example of a triangular mesh surface approximation.

FIG. 29B shows an example of a surface approximation by packing with 3Dshapes (shown as capsules) to approximate a surface and some or all ofthe internal volume of a three-dimensional object (or the portion of theobject adjacent to a second object).

FIG. 29C is an example of a comparison of a tooth having a surfaceapproximated by both a triangular mesh (on right) and packing with 3Dshapes (on left, shown as capsules).

FIGS. 30A-30C illustrate cross-sections through examples of 3D shapeshaving a core that is a constant radius from the core. In FIG. 30A the3D shape is a sphere, showing a point as the core. In FIG. 30B, the 3Dshape is a capsule, having a line and an outer surface that is constantradius from the line. FIG. 30C shows an example of a rectangular corehaving a constant radius from the square.

FIGS. 31A-31C show exemplary 3D shapes corresponding to those shown inFIGS. 30A-30C, respectively. In FIG. 31A the 3D shape is a sphere. InFIG. 31B, the 3D shape is a capsule. In FIG. 31C the 3D shape is arounded rectangle.

FIGS. 32A and 32B illustrate top and side perspective views,respectively, of digital models of molars having outer surfaces thathave been modeled by packing the surfaces with capsules.

FIGS. 33A-33B illustrate left and right side perspective views,respectively, of digital models of a portion of dental device (shown asprecision wings) having outer surfaces that have been modeled by packingthe surfaces with capsules.

FIG. 34A illustrates another example of a tooth having a first (left)side surface that is formed from the digital model of the tooth bypacking a plurality of 3D shapes (capsules in this example) toapproximate the surface.

FIG. 34B illustrate a digital model of a plurality of the patient'steeth (shown here as the patient's maxillary arch) in which each toothhas been divided up into regions (e.g., left and right or left, rightand middle regions) so that the surface of the tooth in each region canbe modeled (e.g., formed) by packing a plurality of 3D shapes (e.g.,capsules) to approximate the surface.

FIG. 35A illustrates one example illustrating the formation of ahierarchy of bounding boxes around capsules.

FIG. 35B is an example showing the tiers of the exemplary hierarchy ofFIG. 35A, forming a tree hierarchy.

FIG. 36 is an example of pseudo-code for traversal of a bounding boxhierarchy to skip distance calculation between capsules that cannotinfluence the final value of collisions between two surfaces.

FIG. 37A illustrates one method of determining collision distance (inthis example, negative collision distance or spacing) between twocapsules from each of two separate surfaces being examined forcollisions.

FIG. 37B is an example of pseudo code for finding approximate distancebetween the surfaces of two shapes (e.g., shape A and shape B) packedwith capsules.

FIG. 38 is an example of a digital model of a set of teeth, including apair of teeth shown colliding.

FIG. 39 is an enlarged view of the collision region between the twocolliding teeth shown in FIG. 38.

FIG. 40 is an enlarged view of one of the teeth shown colliding in FIG.38, illustrating the six axes for which a velocity of collision may bedetermined.

FIG. 41A shows one example of a pair of tooth shapes showing regionshaving close (closed) curvatures.

FIG. 41B is a 3D model of a patient's teeth showing regions having close(closed) curvatures.

FIG. 41C is a comparison between moderate precision (left) and highprecision (right) estimation of tooth volume for collision estimationusing different ‘capsule filling’ techniques described herein.

FIG. 42 illustrates one example of a mock-up of a user interfacedisplay, configured as a concurrent (side-by-side) display of treatmentplan “cards”, also referred to herein as a multiple card view.

FIG. 43A is a table (Table 1) showing rankings of treatment plansindexed by attachments (all, posterior only, none) and interproximalreduction (IPR used, IPR not used) for single arch treatment plans. Thevalue represents the relative rank of comprehensiveness (1 is highest).

FIG. 43B is a table (Table 2) showing rankings of treatment plansindexed by attachments (all, posterior only, none) and interproximalreduction (IPR used, IPR not used) for dual arch treatment plans. Thevalue represents the relative rank of comprehensiveness (1 is highest).

FIG. 44 is another example of a user interface display, illustrating theuse of treatment plan filters allowing the user to switch or togglebetween different treatment plans for display. In FIG. 44, a controlconfigured as a drop-down menu or filter allows the user to switchbetween the type of attachments (e.g., all attachments, no attachmentsor poster-only attachments.

FIG. 45 is another example of a user interface display, illustrating theuse of treatment plan filters allowing the user to switch or togglebetween different treatment plans for display.

FIG. 46 illustrates an example of a detailed view of a single treatmentplan, showing the tooth (and any modifications to the teeth, includingattachments, IPR, etc.) for a selected stage of the treatment plan.

FIG. 47 is another example of a multiple treatment plan (MTP) userinterface similar to that shown in FIGS. 42, 44 and 45, above.

FIG. 48 is an example of a single treatment plan (STP) user interface,similar to that shown in FIG. 46, allowing detailed review of atreatment plan and toggling between other treatment plans.

FIG. 49 is another example of an STP user interface.

DETAILED DESCRIPTION

In general, described herein are methods and apparatuses formanufacturing a series of aligners for a patient's teeth that mayinclude generating multiple treatment plans that are limited variousspecified stages (e.g., 5 stages, 6 stages, 7 stages, 8 stages, 9stages, 10 stages, 10 stages, 12 stages, 14 stages, 15 stages, 16stages, 17 stages, 18 stages, 19 stages, 20 stages, 21 stages, 22stages, 23 stages, 24 stages, 25 stages, 26 stages, 27 stages, 28stages, 29 stages, 30 stages, etc.) and variations of these fixed-stagetreatment plans in which one or more features are included to apredetermined degree (e.g., interproximal reduction, use of some numberof aligner attachments, etc.). These methods and apparatuses may alsoinclude interactively displaying the multiple treatment plans, andallowing a user, such as a dental professional (e.g., doctor, dentist,orthodontist, etc.) to view, select and/or modify the multiple treatmentplans. The multiple treatment plans may be labeled to indicate whattreatment goals they do or do not address. The user may also select asubset of the multiple treatment plans for inclusion as part of apatient consultation, displaying the treatment plans for comparison andselection by patient.

A treatment plan optimizing generator, described in greater detailbelow, may be used to generate a plurality of treatment plans that arevariations of each other. Typically the input to the treatment planoptimizing generator is a digital scan of the patient's teeth, as wellas the constraints (e.g., number of stages, tooth modificationsfeatures, etc.) and preferences, and an “ideal” alignment of thepatient's teeth (which may be manually, automatically orsemi-automatically generated). The treatment plan optimizing generatormay then automatically generate a treatment plan that is limited bythose constraints, and that both addresses one or more treatment goals(which may also be identified or automatically identified) and is asclose to the ideal alignment as possible. The treatment plan optimizinggenerator may be used multiple times to automatically generate aplurality of treatment plan variations that may be collected into anarray (or group) of treatment plans.

As will be described in greater detail here, the results of the multipletreatment plan generation may be presented to a user. The multipletreatment plans may be collected as an array of multiple treatment plansthat may include metadata identifying each treatment plan and/or thetreatment goal that it addresses or does not address. Each treatmentplan may represent a clinically feasible treatment plan. Further, foreach plan there may be several options available to modify the plan.Plans may be limited to the number of stages, which may correlate to acommercial product. The product may include restrictions (productlimitations) which may be included in the treatment plan. For exampletreatment plans may correspond to low stage plans (e.g. between 5 and 13stages), intermediate stage plans (between 14 and 25 stages) and highintermediate stage plans (26 and more stages). Other tooth modificationfeatures may also be included as limitations modifying the treatmentplans, such as including or not including aligner attachment placement.If attachments are not allowed, then a restricted clinical protocol maybe applied to avoid unpredictable movements. Another example of a toothmodification feature that may be included in the treatment plan is toinclude IPR or not include IPR. If IPR is not allowed then the best planmay be presented with a condition that IPR is not allowed during theduration of the treatment.

In addition, template selection may select a clinical protocol to beapplied for plan generation. The user may select any combination ofoptions in order to determine which treatment plan is the best, giventhe constraints provided. All possible combinations of the plans arepre-calculated so the user can see, in real time, the options availableby changing to a different clinical filter without the need to redo thetreatment plan. The user may also modify any of the treatment plans with3D controls, in which each change made with tools modifies a plan but isconfigured to keeps the ability to transfer the selected (and modified)treatment plan directly to manufacturing (e.g., without further humanintervention).

In general, the methods described here are directed to the manufactureof a series or sequence of orthodontic aligner appliances that maybeworn sequentially to correct malocclusion(s). For example, FIG. 1illustrates an exemplary tooth repositioning appliance or aligner 100that can be worn by a patient in order to achieve an incrementalrepositioning of individual teeth 121 in the jaw. The appliance caninclude a shell 110 (e.g., a continuous polymeric shell or a segmentedshell) having teeth-receiving cavities 111 that receive and resilientlyreposition the teeth 121. An appliance or portion(s) thereof may beindirectly fabricated using a physical model of teeth. For example, anappliance (e.g., polymeric appliance) can be formed using a physicalmodel of teeth and a sheet of suitable layers of polymeric material. Insome embodiments, a physical appliance is directly fabricated, e.g.,using additive manufacturing techniques, from a digital model of anappliance. An appliance can fit over all teeth present in an upper orlower jaw, or less than all of the teeth. The appliance can be designedspecifically to accommodate the teeth of the patient (e.g., thetopography of the tooth-receiving cavities matches the topography of thepatient's teeth), and may be fabricated based on positive or negativemodels of the patient's teeth generated by impression, scanning, and thelike. Alternatively, the appliance can be a generic appliance configuredto receive the teeth, but not necessarily shaped to match the topographyof the patient's teeth. In some cases, only certain teeth received by anappliance may be repositioned by the appliance while other teeth canprovide a base or anchor region for holding the appliance in place as itapplies force against the tooth or teeth targeted for repositioning. Insome cases, some or most, and even all, of the teeth may be repositionedat some point during treatment. Teeth that are moved can also serve as abase or anchor for holding the appliance as it is worn by the patient.No wires or other means may be necessary for holding an appliance inplace over the teeth. In some cases, however, it may be desirable ornecessary to provide individual attachments or other aligner featuresfor controlling force delivery and distribution Exemplary appliances,including those utilized in the Invisalign® System, are described innumerous patents and patent applications assigned to Align Technology,Inc. including, for example, in U.S. Pat. Nos. 6,450,807, and 5,975,893,as well as on the company's website, which is accessible on the WorldWide Web (see, e.g., the url “invisalign.com”). Examples oftooth-mounted attachments suitable for use with orthodontic appliancesare also described in patents and patent applications assigned to AlignTechnology, Inc., including, for example, U.S. Pat. Nos. 6,309,215 and6,830,450.

Optionally, in cases involving more complex movements or treatmentplans, it may be beneficial to utilize auxiliary components (e.g.,features, accessories, structures, devices, components, and the like) inconjunction with an orthodontic appliance. Examples of such accessoriesinclude but are not limited to elastics, wires, springs, bars, archexpanders, palatal expanders, twin blocks, occlusal blocks, bite ramps,mandibular advancement splints, bite plates, pontics, hooks, brackets,headgear tubes, springs, bumper tubes, palatal bars, frameworks,pin-and-tube apparatuses, buccal shields, buccinator bows, wire shields,lingual flanges and pads, lip pads or bumpers, protrusions, divots, andthe like. Additional examples of accessories include but are not limitedto opposing arch features, occlusal features, torsional rigidityfeatures, occlusal cusp, and bridges. In some embodiments, theappliances, systems and methods described herein include improvedorthodontic appliances with integrally formed features that are shapedto couple to such auxiliary components, or that replace such auxiliarycomponents.

FIG. 1B illustrates a tooth repositioning system 110 including aplurality of appliances 112, 114, 116. Any of the appliances describedherein can be designed and/or provided as part of a set of a pluralityof appliances used in a tooth repositioning system. Each appliance maybe configured so a tooth-receiving cavity has a geometry correspondingto an intermediate or final tooth arrangement intended for theappliance. The patient's teeth can be progressively repositioned from aninitial tooth arrangement towards a target tooth arrangement by placinga series of incremental position adjustment appliances over thepatient's teeth. For example, the tooth repositioning system 110 caninclude a first appliance 112 corresponding to an initial tootharrangement, one or more intermediate appliances 114 corresponding toone or more intermediate arrangements, and a final appliance 116corresponding to a target arrangement. A target tooth arrangement can bea planned final tooth arrangement selected for the patient's teeth atthe end of all planned orthodontic treatment. Alternatively, a targetarrangement can be one of some intermediate arrangements for thepatient's teeth during the course of orthodontic treatment, which mayinclude various different treatment scenarios, including, but notlimited to, instances where surgery is recommended, where interproximalreduction (IPR) is appropriate, where a progress check is scheduled,where anchor placement is best, where palatal expansion is desirable,where restorative dentistry is involved (e.g., inlays, onlays, crowns,bridges, implants, veneers, and the like), etc. As such, it isunderstood that a target tooth arrangement can be any planned resultingarrangement for the patient's teeth that follows one or more incrementalrepositioning stages. Likewise, an initial tooth arrangement can be anyinitial arrangement for the patient's teeth that is followed by one ormore incremental repositioning stages.

FIG. 1C illustrates a method 150 of orthodontic treatment using aplurality of appliances, in accordance with embodiments. The method 150can be practiced using any of the appliances or appliance sets describedherein. In step 160, a first orthodontic appliance is applied to apatient's teeth in order to reposition the teeth from a first tootharrangement to a second tooth arrangement. In step 170, a secondorthodontic appliance is applied to the patient's teeth in order toreposition the teeth from the second tooth arrangement to a third tootharrangement. The method 150 can be repeated as necessary using anysuitable number and combination of sequential appliances in order toincrementally reposition the patient's teeth from an initial arrangementtowards a target arrangement. The appliances can be generated all at thesame stage or in sets or batches (e.g., at the beginning of a stage ofthe treatment), or the appliances can be fabricated one at a time, andthe patient can wear each appliance until the pressure of each applianceon the teeth can no longer be felt or until the maximum amount ofexpressed tooth movement for that given stage has been achieved. Aplurality of different appliances (e.g., a set) can be designed and evenfabricated prior to the patient wearing any appliance of the plurality.After wearing an appliance for an appropriate period of time, thepatient can replace the current appliance with the next appliance in theseries until no more appliances remain. The appliances are generally notaffixed to the teeth and the patient may place and replace theappliances at any time during the procedure (e.g., patient-removableappliances). The final appliance or several appliances in the series mayhave a geometry or geometries selected to overcorrect the tootharrangement. For instance, one or more appliances may have a geometrythat would (if fully achieved) move individual teeth beyond the tootharrangement that has been selected as the “final.” Such over-correctionmay be desirable in order to offset potential relapse after therepositioning method has been terminated (e.g., permit movement ofindividual teeth back toward their pre-corrected positions).Over-correction may also be beneficial to speed the rate of correction(e.g., an appliance with a geometry that is positioned beyond a desiredintermediate or final position may shift the individual teeth toward theposition at a greater rate). In such cases, the use of an appliance canbe terminated before the teeth reach the positions defined by theappliance. Furthermore, over-correction may be deliberately applied inorder to compensate for any inaccuracies or limitations of theappliance.

The various embodiments of the orthodontic appliances presented hereincan be fabricated in a wide variety of ways. In some embodiments, theorthodontic appliances herein (or portions thereof) can be producedusing direct fabrication, such as additive manufacturing techniques(also referred to herein as “3D printing) or subtractive manufacturingtechniques (e.g., milling). In some embodiments, direct fabricationinvolves forming an object (e.g., an orthodontic appliance or a portionthereof) without using a physical template (e.g., mold, mask etc.) todefine the object geometry. For example, stereolithography can be usedto directly fabricate one or more of the appliances herein. In someembodiments, stereolithography involves selective polymerization of aphotosensitive resin (e.g., a photopolymer) according to a desiredcross-sectional shape using light (e.g., ultraviolet light). The objectgeometry can be built up in a layer-by-layer fashion by sequentiallypolymerizing a plurality of object cross-sections. As another example,the appliances herein can be directly fabricated using selective lasersintering. In some embodiments, selective laser sintering involves usinga laser beam to selectively melt and fuse a layer of powdered materialaccording to a desired cross-sectional shape in order to build up theobject geometry. As yet another example, the appliances herein can bedirectly fabricated by fused deposition modeling. In some embodiments,fused deposition modeling involves melting and selectively depositing athin filament of thermoplastic polymer in a layer-by-layer manner inorder to form an object. In yet another example, material jetting can beused to directly fabricate the appliances herein. In some embodiments,material jetting involves jetting or extruding one or more materialsonto a build surface in order to form successive layers of the objectgeometry.

In some embodiments, the direct fabrication methods provided hereinbuild up the object geometry in a layer-by-layer fashion, withsuccessive layers being formed in discrete build steps. Alternatively orin combination, direct fabrication methods that allow for continuousbuild-up of an object's geometry can be used, referred to herein as“continuous direct fabrication.” Various types of continuous directfabrication methods can be used. Continuous liquid interphase printingis described in U.S. Patent Publication Nos. 2015/0097315, 2015/0097316,and 2015/0102532, the disclosures of each of which are incorporatedherein by reference in their entirety.

As another example, a continuous direct fabrication method can achievecontinuous build-up of an object geometry by continuous movement of thebuild platform (e.g., along the vertical or Z-direction) during theirradiation phase, such that the hardening depth of the irradiatedphotopolymer is controlled by the movement speed. Accordingly,continuous polymerization of material on the build surface can beachieved. Such methods are described in U.S. Pat. No. 7,892,474, thedisclosure of which is incorporated herein by reference in its entirety.

In another example, a continuous direct fabrication method can involveextruding a composite material composed of a curable liquid materialsurrounding a solid strand. The composite material can be extruded alonga continuous three-dimensional path in order to form the object. Suchmethods are described in U.S. Patent Publication No. 2014/0061974, thedisclosure of which is incorporated herein by reference in its entirety.

In yet another example, a continuous direct fabrication method utilizesa “heliolithography” approach in which the liquid photopolymer is curedwith focused radiation while the build platform is continuously rotatedand raised. Accordingly, the object geometry can be continuously builtup along a spiral build path. Such methods are described in U.S. PatentPublication No. 2014/0265034, the disclosure of which is incorporatedherein by reference in its entirety.

In some embodiments, relatively rigid portions of the orthodonticappliance can be formed via direct fabrication using one or more of thefollowing materials: a polyester, a co-polyester, a polycarbonate, athermoplastic polyurethane, a polypropylene, a polyethylene, apolypropylene and polyethylene copolymer, an acrylic, a cyclic blockcopolymer, a polyetheretherketone, a polyamide, a polyethyleneterephthalate, a polybutylene terephthalate, a polyetherimide, apolyethersulfone, and/or a polytrimethylene terephthalate.

In some embodiments, relatively elastic portions of the orthodonticappliance can be formed via direct fabrication using one or more of thefollowing materials: a styrenic block copolymer (SBC), a siliconerubber, an elastomeric alloy, a thermoplastic elastomer (TPE), athermoplastic vulcanizate (TPV) elastomer, a polyurethane elastomer, ablock copolymer elastomer, a polyolefin blend elastomer, a thermoplasticco-polyester elastomer, and/or a thermoplastic polyamide elastomer.

Optionally, the direct fabrication methods described herein allow forfabrication of an appliance including multiple materials, referred toherein as “multi-material direct fabrication.” In some embodiments, amulti-material direct fabrication method involves concurrently formingan object from multiple materials in a single manufacturing step usingthe same fabrication machine and method. For instance, a multi-tipextrusion apparatus can be used to selectively dispense multiple typesof materials (e.g., resins, liquids, solids, or combinations thereof)from distinct material supply sources in order to fabricate an objectfrom a plurality of different materials. Such methods are described inU.S. Pat. No. 6,749,414, the disclosure of which is incorporated hereinby reference in its entirety. Alternatively or in combination, amulti-material direct fabrication method can involve forming an objectfrom multiple materials in a plurality of sequential manufacturingsteps. For instance, a first portion of the object can be formed from afirst material in accordance with any of the direct fabrication methodsherein, then a second portion of the object can be formed from a secondmaterial in accordance with methods herein, and so on, until theentirety of the object has been formed.

In many embodiments, post-processing of appliances includes cleaning,post-curing, and/or support removal processes. Relevant post-processingparameters can include purity of cleaning agent, cleaning pressureand/or temperature, cleaning time, post-curing energy and/or time,and/or consistency of support removal process. These parameters can bemeasured and adjusted as part of a process control scheme. In addition,appliance physical properties can be varied by modifying thepost-processing parameters. Adjusting post-processing machine parameterscan provide another way to compensate for variability in materialproperties and/or machine properties.

Although various embodiments herein are described with respect to directfabrication techniques, it shall be appreciated that other techniquescan also be used, such as indirect fabrication techniques. In someembodiments, the appliances herein (or portions thereof) can be producedusing indirect fabrication techniques, such as by thermoforming over apositive or negative mold. Indirect fabrication of an orthodonticappliance can involve one or more of the following steps: producing apositive or negative mold of the patient's dentition in a targetarrangement (e.g., by additive manufacturing, milling, etc.),thermoforming one or more sheets of material over the mold in order togenerate an appliance shell, forming one or more structures in the shell(e.g., by cutting, etching, etc.), and/or coupling one or morecomponents to the shell (e.g., by extrusion, additive manufacturing,spraying, thermoforming, adhesives, bonding, fasteners, etc.).Optionally, one or more auxiliary appliance components as describedherein (e.g., elastics, wires, springs, bars, arch expanders, palatalexpanders, twin blocks, occlusal blocks, bite ramps, mandibularadvancement splints, bite plates, pontics, hooks, brackets, headgeartubes, bumper tubes, palatal bars, frameworks, pin-and-tube apparatuses,buccal shields, buccinator bows, wire shields, lingual flanges and pads,lip pads or bumpers, protrusions, divots, etc.) are formed separatelyfrom and coupled to the appliance shell (e.g., via adhesives, bonding,fasteners, mounting features, etc.) after the shell has been fabricated.

The orthodontic appliances herein can be fabricated using a combinationof direct and indirect fabrication techniques, such that differentportions of an appliance can be fabricated using different fabricationtechniques and assembled in order to form the final appliance. Forexample, an appliance shell can be formed by indirect fabrication (e.g.,thermoforming), and one or more structures or components as describedherein (e.g., auxiliary components, power arms, etc.) can be added tothe shell by direct fabrication (e.g., printing onto the shell).

The configuration of the orthodontic appliances herein can be determinedaccording to a treatment plan for a patient, e.g., a treatment planinvolving successive administration of a plurality of appliances forincrementally repositioning teeth. Computer-based treatment planningand/or appliance manufacturing methods can be used in order tofacilitate the design and fabrication of appliances. For instance, oneor more of the appliance components described herein can be digitallydesigned and fabricated with the aid of computer-controlledmanufacturing devices (e.g., computer numerical control (CNC) milling,computer-controlled additive manufacturing such as 3D printing, etc.).The computer-based methods presented herein can improve the accuracy,flexibility, and convenience of appliance fabrication.

The methods and apparatuses described herein may form, or beincorporated into a computer-based 3-dimensional planning/design tool,and may be used to design and fabricate the orthodontic appliancesdescribed herein.

FIG. 2A shows one example of a treatment plan solver (e.g., an automatedorthodontic treatment planning system, or solver) 101 that may be usedto automatically generate a series of treatment plans and thereforemanufacture a series of aligners based on one of the series of treatmentplans.

The solver 101 may include a variety of modules, including engines,processors on which the engines may operate, and/or one or moredatastores. A computer system can be implemented as an engine, as partof an engine or through multiple engines. As used herein, an engine mayinclude one or more processors or a portion thereof. A portion of one ormore processors can include some portion of hardware less than all ofthe hardware comprising any given one or more processors, such as asubset of registers, the portion of the processor dedicated to one ormore threads of a multi-threaded processor, a time slice during whichthe processor is wholly or partially dedicated to carrying out part ofthe engine's functionality, or the like. As such, a first engine and asecond engine can have one or more dedicated processors or a firstengine and a second engine can share one or more processors with oneanother or other engines. Alternatively or additionally, differentengines may share the same processor. Depending uponimplementation-specific or other considerations, an engine can becentralized or its functionality distributed. An engine can includehardware, firmware, or software embodied in a computer-readable mediumfor execution by the processor. The processor transforms data into newdata using implemented data structures and methods, such as is describedwith reference to the figures herein.

The engines described herein, or the engines through which the systemsand devices described herein can be implemented, can be cloud-basedengines. As used herein, a cloud-based engine is an engine that can runapplications and/or functionalities using a cloud-based computingsystem. All or portions of the applications and/or functionalities canbe distributed across multiple computing devices, and need not berestricted to only one computing device. In some embodiments, thecloud-based engines can execute functionalities and/or modules that endusers access through a web browser or container application withouthaving the functionalities and/or modules installed locally on theend-users' computing devices.

As used herein, datastores are intended to include repositories havingany applicable organization of data, including tables, comma-separatedvalues (CSV) files, traditional databases (e.g., SQL), or otherapplicable known or convenient organizational formats. Datastores can beimplemented, for example, as software embodied in a physicalcomputer-readable medium on a specific-purpose machine, in firmware, inhardware, in a combination thereof, or in an applicable known orconvenient device or system. Datastore-associated components, such asdatabase interfaces, can be considered “part of” a datastore, part ofsome other system component, or a combination thereof, though thephysical location and other characteristics of datastore-associatedcomponents is not critical for an understanding of the techniquesdescribed herein.

Datastores can include data structures. As used herein, a data structureis associated with a particular way of storing and organizing data in acomputer so that it can be used efficiently within a given context. Datastructures are generally based on the ability of a computer to fetch andstore data at any place in its memory, specified by an address, a bitstring that can be itself stored in memory and manipulated by theprogram. Thus, some data structures are based on computing the addressesof data items with arithmetic operations; while other data structuresare based on storing addresses of data items within the structureitself. Many data structures use both principles, sometimes combined innon-trivial ways. The implementation of a data structure usually entailswriting a set of procedures that create and manipulate instances of thatstructure. The datastores, described herein, can be cloud-baseddatastores. A cloud-based datastore is a datastore that is compatiblewith cloud-based computing systems and engines.

In FIG. 2A the system for automatically creating an orthodontictreatment plan of a patient may include one or more processors 102. Thetreatment plan solver set of instructions may operate on the one or moreprocessors. The system may also include a collision detector 106, whichmay also operate on the one or more processors. The system may alsoinclude a memory that is part of or coupled to the one or moreprocessors, and which stores computer-program instructions, that, whenexecuted by the one or more processors, perform a computer-implementedmethod that may include collecting (e.g., forming, reading, receiving,etc.) a digital model of a surface for each tooth of a plurality of apatient's teeth by packing a plurality of 3D shapes to approximate(e.g., model, form, etc.) the surface for each tooth, wherein the 3Dshapes each have a core that is a line segment or a closed plane figureand an outer surface that is a constant radius from the core. As will bedescribed in greater detail below, the collision detector 106 mayinclude hardware, software and/or firmware for packing the tooth orother feature, and modeling the surface with the 3D shapes such as thecapsules. The system may also be configured to collect (e.g., toreceive, read, etc.) treatment preferences. The preferences may becollected into a treatment preference datastore 115. The preferences mayalso include treatment details datastore 117. The system may form, forthe surface for each tooth of the plurality of the patient's teeth, ahierarchy of bounding boxes enclosing the plurality of 3D shapes. Thismay be performed using the processor and/or as part of the collisiondetector. The tooth positions for the plurality of the patient's teethmay be passed from a treatment plan solver 101 to a collision detector(see, e.g., FIG. 2B. The solver may collect a digital model of thepatient's teeth to be modified by the treatment plan (collecting mayinclude receiving/loading from an external source, retrieving from amemory, including a patient teeth datastore 123 or other memory, or thelike).

The one or more processors 102 or any of the other elements (e.g.,numeric function engine 107, numeric function building engine 109,comprehensive final position engine 111, collision detector 106,solution vector mapping engine 113, etc.) may be connected in anyappropriate manner and any of these elements may also be connected tothe datastores (e.g., patient teeth datastore 123, treatment targetsdatastore 119, treatment details datastore 117, treatment preferencesdatastore 115, and numeric limits datastore 121, etc.).

The numeric function building engine 109 may be used to select aplurality of numerically expressed treatment targets (e.g., from atreatment targets datastore 119 or other memory or input accessible tothe one or more processors) based on the set of treatment details (whichmay be accessed from the treatment details datastore 117 or otheraccessible memory/input), the set of treatment preferences (which may beprovided by the treatment preferences datastore 115 or othermemory/input) and the comprehensive final position of the patient'steeth. The comprehensive final position of the patient's teeth may beprovided by the comprehensive final position engine 111 or from a memorystoring the comprehensive final position.

The solver may also include a numeric function minimizing engine 107which may combine the plurality of numerically expressed treatmenttargets to form a single numerical function. This single numericalfunction may then be minimized to solve for one or more solution vectorsusing the collision detector 106 and a set of numeric limits that may beprovided, for example, from a numeric limits datastore 121 or othermemory/input. The numeric limits may be selected for the singlenumerical function based on the set treatment preferences (e.g., fromthe treatment preferences datastore 115 or other memory/input).

The solution vector typically includes all of the stages forming thetreatment plan, and may be stored in a memory, and/or displayed, and/ortransferred. In some variations the solution vector may be convertedinto a treatment plan using a solution vector mapping engine 113 to mapthe solution vector to a treatment plan, wherein the treatment planincludes a final tooth position that is different from the comprehensivefinal position of the patient's teeth.

FIG. 2C schematically illustrates a method of creating a treatment planto align a patient's teeth using a plurality of removable aligners to beworn in sequential stages. In this example, the first step is to collecta digital model of a patient's teeth (e.g., upper or lower or both upperand lower arch) 250. This may include, for example, receiving, in aprocessor, a digital model of a patient's teeth. The method may alsoinclude selecting a plurality of numerically expressed treatment targets(e.g., based on a selected set of treatment details, a set of treatmentpreferences, and a comprehensive final position of the teeth) 252. Theplurality of numerically expressed targets may then be combined into asingle numerical function 254, and a plurality of numeric limits on thesingle numeric function (e.g., based on a set of treatment preferences)may be selected 256. The single numeric function may be minimizedsubject to the plurality of numeric limits to get a solution vector(including all stage form the treatment plan, use automatic collisiondetection) 258. The process of solving (minimizing) for the solutionvector may implement the collisions detection method (FIG. 2D, describedin greater detail below). The solution vector may then be mapped to atreatment plan 260.

Method of Manufacturing a Series of Aligners

FIG. 3 is an overview of a method for manufacturing a series of alignersfor a “partial treatment” plan. A partial treatment plan is a plan forwhich only a limited series of aligners is used to treat the patient;this limited number of aligners may be a predetermined number (e.g., 7,10, 12, 16, 26, etc.) that is less than the total number that it maytake to optimally correct the patient's malocclusions fully, addressingall of the clinically resolvable conditions (also referred to astreatment goals). In a partial treatment plan, the fixed number ofaligners in the series may be configured (by configuring the treatmentplan) to instead address some of the treatment goals within the limitednumber of stages defined, and approaching as closely as possible to theideal realigned configuration without either creating new malocclusionsor exacerbating existing malocclusions.

In FIG. 3, the method starts by collecting from the patient (and by theuser, e.g., dental professional), a model of the patient's teeth 303, aswell as any conditions (e.g., tooth movement restrictions) orpreferences for treatment 301; the method or apparatus may alsooptionally identify any general preferences that are specific to thedental processional 302, and that may be applied to all of that dentalprofessional's patients. In addition (and optionally) the method orapparatus may also provide an indication of the type of dental product(e.g., the type of dental/orthodontic products to be used to treat thepatient 304. All of this information, and particularly the prescriptioninformation, may be completed in a relatively short (e.g., 2-25, 2-20,2-15, etc. lines) form or virtual survey. The user may submit thisinformation to a treatment plan optimizing generator, which may belocated at a remote site. The treatment plan optimizing generator, whichis described in detail below, may use this information to generate aplurality of treatment plans. For example, the treatment plan optimizinggenerator may first prepare the model 305, e.g., by digitizing it if itis not already a digital model, and by segmenting the digital model intoindividual teeth, gingiva, etc. Once prepared, the automated treatmentplanning 307 may be performed to automatically generate multipletreatment plans using, e.g., different numbers of stages; for each stagemultiple variations including different treatment properties (e.g., IPR,attachments, etc.) may also be generated 311. Each treatment plan iscomplete, and may be used to build an aligner series. For example, eachtreatment plan may include a new (and potentially unique) final positionfor the patient's teeth at the end of the treatment, staging showing thetooth movement and speed of movement for each stage (e.g., key frames)and a set of aligner features 313. The corresponding aligner featuresmay include the location of the attachments, etc.

This automated treatment planning may therefore use a treatment planoptimizing generator multiple times, each time providing slightlydifferent treatment details and/or targets, while annotating eachtreatment plan with an indicator of what constraints and/or treatmenttargets were used to generate that treatment plan, including, forexample, the fixed number of stages. The resulting multiple treatmentplans may be collected into a single set (e.g., an array) and all ofthese treatment plans submitted back to the user via, e.g., a userinterface to provide meaningful and interactive display, selectionand/or manipulation of the treatment plans 315. The user (e.g., dentalprofessional) may then, using the interactive display, in real time,toggle between the multiple plans, and select one or a subset oftreatment plans 319. Optionally, the user may modify one or more plans319; if the user modifies a treatment plan in a manner that exceed thepre-calculated plurality of treatment plans 321, then the modificationsmay be transmitted to back to the automated treatment planning subsystem(including the treatment plan optimizing generator) to generateadditional treatment plans including the user's modifications 337. Thesenew treatment plans may replace or supplement the plans alreadypre-calculated.

Optionally, once a subset of treatment plans has been selected from thelarger array of treatment plans, the user may present the subset oftreatment plans to a subject 323. The subject may be consulted toprovide an indication (e.g., by showing the final stage/teeth position)of the orthodontic effect achievable by each treatment plan. Either theuser or the subject (or both) may decide which treatment plan to choose,and the selected treatment plan may be forwarded on forfabrication/manufacturing 325 as discussed above.

FIG. 4 provides additional detail on one example of a consultation modeof operation of the system described herein. In this example, after thedental professional has selected two or more dental pans 419 (see alsoFIG. 3, 319), two or more of these dental plans may be presented to thepatient 433, allowing the patient to select between them. In addition tothe image(s) of the teeth, including at least the last positon of thetreatment plan, in some examples, metadata indicating the number ofstages/length of treatment, and/or the treatment properties used togenerate the particular treatment plan, etc., may be displayed as well.The display may be side-by-side 435 or it may be sequential, etc. Thepatient may then select between the presented plans 435. Finally, andoptionally, the user may finalize the treatment, and the selectedtreatment plan may be submitted for manufacturing 437.

FIGS. 5 and 6 provide more detailed examples of possible methods formanufacturing a sequence of aligners for a patient. In FIG. 5, the useris presumed to be a doctor, through the user may be any dentalprofessional. The user may first open a record for the patient,including any photos, using a user interface (IDS, a portal that theuser may log into to access an account). A preliminary (automatic ormanual) assessment may be performed to determine if the patient is agood candidate for the procedure (“case assessment”), and the user mayreview the case assessment. Thereafter, the user may submit a minimalpatient prescription (e.g., indicating treatment goals, constraints,etc.). The user may further submit a model of the patient's teeth to theremote site for processing as mentioned above, to produce a digitalmodel that is adequate for automatic treatment pan generation. In somecases a technician may perform digital “detailing” of the digital modelto prepare it for processing. The treatment plan optimizing generatormay then be used to automatically generate an array of alternativetreatment plans (MTP) as discussed above. Thereafter, a user interfaceconfigured to allow interactive display of a plurality of differentalternative treatment plans (“CCWeb”) may be used to review and select,and in some variations, modify, the treatment plans in the array oftreatment plans. The patient may be consulted, as discussed above. Oncethe user selects a single treatment plan, and is satisfied with thetreatment plan, the user may then transmit the selected treatment planto the manufacturer (technician) who may (optionally) review and send afinalized version of the treatment plan for final approval. Onceapproved, the treatment plan, including all of the stages of aligners,may be fabricated using the treatment plan either directly or convertingit into a manufacturing format. If the user is not satisfied with thetreatment plan, it may be modified.

FIG. 6 shows a similar work flow to that shown in FIG. 5. In FIG. 6, theuser is presumed to provide the digital model of the patient's teeth atthe start (e.g., by digitally scanning the patient's teeth).

FIGS. 7A and 7B illustrate examples of an interactive display of aplurality of treatment plans to allow a user to select between thetreatment plans and/or modify the treatment plans as quickly andefficiently as possible. In FIG. 7A, the display shows the final stage(final configuration) of each of the plurality of treatment plans. Inthis example, the plans are aligned side-by-side based on the number ofstages (n₁, n₂, . . . n_(x)). Each of these plans also includes optionalvariants (option 1, option 2, etc.) which may be displayed when the usercontrol (box) is selected, which may be indicated by a check, as shownin FIG. 7A.

FIG. 7B is similarly to FIG. 7A, but lists each treatment plan as partof a ribbon that may be moved by sliding left or right, for example. Anyof these user interfaces may show additional representations of thestages, either as key frames and/or as tooth representations.

FIG. 7C illustrates an example of a system. This system 701 isconfigured to provide interactive, real-time and dynamic comparisonbetween different treatment plans. In FIG. 7C the system 701 includes aplurality of modules that may operate together in any combination toprovide real-time (or near real-time) interactive, dynamic display forcomparison between multiple full orthodontic treatment plans, includingrapidly toggling between different complete treatment plans toillustrate the differences between treatment plans having modifiedinputs (e.g., with/without IPR, extraction, etc.). For example, in FIG.7C, the system may include a user interface 711 for displaying(side-by-side and/or sequentially) different treatment plans. Thetreatment plans may be calculated as described herein, using a varietyof different treatment preferences and/or treatment details. Thetreatment plans may be arranged in a grouping of any type (e.g., anarray), and may be collected by the system (e.g., received, etc.) from atreatment plan generating system (such as shown in FIG. 2A, above), andmay be stored in a treatment plan datastore 717 for use by the system701. Each treatment plan of the plurality of treatment plans may includea set of sequential stages for orthodontic movement of the patient'steeth including a final stage. The final stage may represent the finalposition of the patient's teeth. In particular, these systems may beused when at least three of the treatment plans have different numbersof sequential stages, and further wherein the array of treatment planscomprises two or more treatment plans having different treatmentproperties. The different treatment properties may be stored for lateruse by the system in the treatment properties datastore 715.

In operation the system may operate the user interface module 711 inconjunction with the user selectable controls 705 to allow the user todynamically switch (toggle) between different treatment plans, which maybe displayed on a screen or other display 703 of the system by showingone or more stages, including the last (final) stage (which may berepresented by a digital model of the patient's teeth in this finalposition), and/or properties of the treatment plan, such as the numberof steps/stages, the duration of treatment, the duration of stages, therates of tooth movements, the movement of the teeth over time (e.g., byanimation or still presentation), etc. The system may display images ofthe teeth at the final stage for each treatment plan of a subset of thetreatment plans from the array of treatment plans on the screen. Atreatment properties switch 709 module may provide real-time (or nearreal time) switching between images of the different treatment planswithin the array of treatment plans, including switching between imagesof the various based on one or more user-selected controls on thescreen.

The system may also include a communications module 713 (e.g., wirelessmodule, such as Wi-Fi, Bluetooth, etc.). The communications module mayallow the system to receive inputs and send outputs, such as, e.g.,transmitting a selected one of the treatment plans for fabrication afterthe user has chosen the selected one of the treatment plans displayed onthe screen.

Any of these systems may also be configured to allow the user to modifyone or more of the treatment plans during the display, includingmodifying tooth position staging timing, etc. In FIG. 7C, the systemincludes an optional Treatment plan modification engine 713 that may beconfigured to allow the user to modify a treatment plan directly.

FIG. 7D illustrates one example of a method of manufacturing a series ofaligners for a patient's teeth. In particularly, this method may allowthe real-time analysis and review of a huge number of treatment plans,selection of one of these treatment plans, and fabrication of a seriesor sequence of aligners based on these treatment plans. For example, themethod may include: gathering (e.g., collecting, including collectingfrom a remote site) an array of treatment plans specific to thepatient's teeth, wherein each treatment plan in the array describes aset of sequential stages for orthodontic movement of the patient's teethincluding a final stage, further wherein at least three of the treatmentplans have different numbers of sequential stages, and further whereinthe array of treatment plans comprises two or more treatment planshaving different treatment properties 721. Images of the teeth after thefinal stage for each treatment plan of a subset of the treatment plansfrom the array of treatment plans may then be displayed on the screen723. The method may then switch, in real time, between images of theteeth at the final stages for different treatment plans within the arrayof treatment plans based on one or more user-selected controls on thescreen 725. Finally, a selected one of the treatment plans forfabrication that the user has chosen may be displayed on the screen andtransmitted for fabrication. Once fabricated they may be sent to thepatient or to the patient's dental/orthodontic provider for distributionto the patient.

FIG. 8A shows another example of a user interface that may be used tointeractively review, modify and/or select a treatment plan. In FIG. 8A,a patient record may be selected, and monitored using the interface. Forexample, the user interface may allow the user to interactively reviewthe plurality of treatment plans generated; the user interface shown inFIG. 8A shows an example in which the patient's teeth model has alreadybeen submitted along with the user preferences, constrains, etc. and thetreatment plan optimizing generator has already been used to generate anarray including a plurality (e.g., 12 or more) of treatment planvariations.

FIG. 8B is another example of a user interface that may be used at thestart of a patient treatment plan. In FIG. 8B, the user interface isconfigured as an interactive prescription form that may allow the user(e.g., clinician, dentist, orthodontist, dental technician, etc.) toselect the patient type (e.g., child, teen, adult), and enterinformation about the patient (e.g., name, age, images, etc.), and/orenter treatment/protocol preferences (e.g., eruption compensation,interproximal reduction preferences, attachment preferences, etc.). Theuser interface may also suggest one or more preferences from a libraryor database of preferences. In some variations the prescription form mayalso allow the user to manually enter treatment preferences. In FIG. 8Bthe prescription form also allows the user to select the type of inputof the patient dentition, such as from an intraoral scan and/or a scanof a mold or impression of a patient's teeth.

FIGS. 9A-9B (similar to FIG. 7A-7B) illustrate a user display that showsthree (in this example) variations, side-by-side, of treatment plans fora patient (“Joe Smith”). As indicated on the right of the userinterface, the patient has upper and lower crowding and an open bite(“malocclusion analysis”). The therapy may be configured to addressthese target goals. In FIG. 9A, the three sets of treatment plans areshown, with user controls allowing selection of variations (that willswap with the variation treatment plan). On the left, a 26 stagetreatment plan is shown; in the middle, a 14 stage treatment plan isshown; on the right, a 7 stage treatment plan is shown. For eachtreatment plan, variations include: with/without IPR, and with/withoutaligner attachments. By selecting the user control on the screen (or onan input such as a keypad, mouse, etc.), the user may see what effectadding/removing these features has. Further, any of these treatmentplans may be selected and put into a subset for display to the subjectas part of a consultation mode. Finally, below the image of the finalstage position of the teeth for each variations is a textual descriptionof the malocclusion analysis specific to that treatment plan. In FIG. 8,all three basic parameters resolved the upper and lower crowding andboth the 26 and 14 stage treatment plans addressed (and partiallyresolved) the open bite malocclusion. FIG. 9B shows the same basic userinterface as FIG. 9A, but with the 26 stage treatment plan shown as avariation including both IPR and aligner attachment.

FIG. 9C is an example of a user interface showing an interactivetreatment planning screen in which a model (3D digital model) of thepatient's dentition is included in a large display window. In somevariations either or both the upper and lower arches are shown aselected stage (or stages) of a treatment plan, and permitting the userto select and apply various digital tools to modify the treatment plan(e.g., changing tooth number, adding/removing or moving attachments,adding/removing/modifying IPR between selected teeth, adding/removingpontics to selected teeth, etc.), manipulate the 3D model of the teeth(e.g., rotate, zoom, show just upper, just lower, both upper and lower,change the angle of display of the tooth to one or more predeterminedangles, etc.), manipulate the display, including selecting a differentstage of the treatment plan and/or show an image of the patient's smileas predicted for any stage (or just the final stage) of the treatmentplan, showing a grip, and/or showing one or more analytics (e.g., Boltonratio, bite analytics, etc.

In FIG. 9C the user interface may also allow the user to both see and tomodify the options applied in generating the treatment plan, includingthe name of the product (e.g., comprehensive, express, teen, etc.)having different properties for the proposed treatment plans. Theproperties (e.g., treatment duration/number of stages, minimal rootmovement, extractions, attachment restrictions, pre-restorative spacers,IPR, expansion (of dental arch) including which teeth to use for each,all, or some subset of these, elastic or surgical simulation,distalization, etc. The user interface of FIG. 9C may allow, asdescribed above, any of the features of claims 9A-9B, includingselecting/deselecting one or more parameters.

FIGS. 9D-9F all illustrate alternative user interfaces as describedherein. In general the term ‘user interface’ may refer to the interfaceseen by the user (doctor, dentist, dental technician, etc.), although,as described below, in some variations any of these user interfaces, orsimilar structures may be presented to the patient, including by theuser, as part of the treatment selection and/or design process and/orduring the treatment process. For example, in FIG. 9D the user interfaceincludes a window for showing one or both of the patient's dental archesat any stage of a proposed treatment plan (e.g., when a single treatmentplan is selected or when only a single treatment plan is generated). Theuser interface may display the characteristics and/or user preferencesthat went into designing the treatment plan, such as the number or rangeof stages (e.g., a comprehensive plan having >21 stages), the amount oftooth movement (minimal or not), a description of the clinical goals(e.g., improving overbite, posterior cross bite, etc.), andaligner/staging features (e.g., pre-restorative spaces, IPR, expansion,proclination, extractions, elastic or surgical, distalization,attachments, etc.). The user interface may also provide 3D tools formanipulating the teeth and/or tools for modifying the treatment plan,and/or resubmitting for generating the new/revised treatment plan orseries of plans. Finally, the user interface may allow the user toselect/accept the treatment plan, so that the series of aligners may betransmitted for manufacture (e.g., which may include one or moreadditional quality control steps).

FIG. 9E is another example of a user interface, similar to that shown inFIG. 9D, but including additional ‘tabs’ allowing the user to selectbetween proposed treatment plans for direct comparison; thefunctionality of the user interface may be otherwise the same asdescribed above. Each treatment plan may be separately or jointlyexamined. In FIG. 9E, the user may toggle between treatment plans; insome variations, as described above, the user may be shown side-by-sidewindows allowing simultaneous comparison between two (or more) treatmentplans, as illustrated in FIG. 9F. In this example a pair of differenttreatment plans generated for the same patient are shown side-by-side;the user may select one or both to rotate (in some variations the userinterface may be allowed to permit either separate rotation of therespective 3D models of the patient's teeth when showing stages of thetreatment plan, or the user interface may be configures so that movingone of the 3D models of the patient's teeth in a particular treatmentplan may automatically move the other 3D model of the patient's teethaccording to the second treatment plan.

In some variations the user interface may be configured to display amodified image of the patient's smile (e.g., the patient's teeth in aforward-facing image of the patient's face) at the conclusion of (or atany stage of) a treatment plan. FIG. 9G shows an image of an initialmalocclusion (left image) for direct side-by-side comparison with asimulated image of the patient's smile following a particular treatmentplan (right image); the specifics of the treatment plan are listed onthe user interface (right side). In this example, the user may togglebetween different treatment plans by toggling (in the controls on theright) various features on or off, such as overbite correction,posterior crossbite correction, molar class correction, overjetcorrection, IPR, attachment positions, number of stages (e.g., product),etc.

As mentioned, in some variations a specific output (including a specificuser interace) for presenting one or more treatment plans to a patientmay be used. FIG. 9H is an example of a patient presentation userinterface that may be provided to the patient to illustrate thepredicted outcome of the treatment, and/or to allow a comparison betweendifferent treatment plans. The user interface in FIG. 9H is a simplifiedversion of the user interfaces discussed above, showing images of thesmile (face) with a simulated patient tooth position, and/or images ofthe patient's teeth. The images may be manipulated by one or morecontrols (e.g., shown on the top of the user interface in FIG. 9H,including zoom, rotate, arch views/angles, etc.). In FIG. 9H, “smile”view is selected and the final tooth arrangement for each of twotreatment plans is shown.

FIGS. 10A-10C illustrate a user display screen including controls fordisplaying one treatment plan in detail, and/or for modifying thetreatment plan. In FIG. 10A a treatment plan having 26 stages is shown.A display of the teeth at each stage is shown in the middle of thescreen and this display may be changed by moving the slider (control1005). One or more controls may also be used to change the view of theteeth shown 1007. Patient information may be shown 1009, as well asproduct information 1011. Treatment details and/or treatment preferencescorresponding to the treatment plan being displayed may also be shown1013. In FIG. 10A, the display indicates that the treatment plan wascreated allowing both interproximal reduction (IPR) and attachments. Theexemplary display shown in FIG. 10A also indicates that this treatmentplan resolves treatment concerns 1015; specifically this treatment planresolves both upper and lower crowding and open bite. In addition, thedisplay also includes a control allowing this treatment plan to be addedto a subset of plans for consultation and/or for selecting this plan toorder 1019. A display such as the one shown in FIG. 10A may be selectedfrom any other display of the treatment plans, such as shown in FIGS.7A-9B.

FIG. 10B shows the display of FIG. 10A in which the treatment plan isbeing modified by the user. In this example the treatment plan is beingmodified to adjust interproximal spacing 1021, shown by the + symbols onthe teeth. In addition, the amount of leveling may also be adjusted.Additional modifications, and tools to control them, may also beincluded. Other controls on the screen may allow the user to communicatedirectly with a technician 1025, or to order a series of aligners basedon this treatment plan 1027, and/or to enter into the consultation mode1031. For example, selection of the control to order the plan may resultin a confirmation screen, such as shown in FIG. 10C.

FIG. 11A shows the exemplary screen of FIG. 10A, configured forcommunication with the technician, as mentioned above. In this example,the user may add instructions or preferences to annotate the treatmentplan for modification. These text notes/instructions may be typed in bythe user, or they may be selected from a menu of notes. In FIG. 11A, theinstructions/notes 1105 include treatment preferences stating: “do notmove upper and lower 3^(rd) molars” and “do not retract upper teeth.”Additional comments may allow the user to submit 1107 or discard 1109the comments. When the treatment preferences are submitted, theapparatus may indicate a confirmation screen 1111 as shown in FIG. 11B.

As mentioned above, the methods and apparatuses (e.g., software,firmware, hardware or some combination of these) may be configured toinclude a consultation mode. FIG. 12 illustrates one example of aconsultation summary screen. This screen may be used by the user beforeentering into a consultation mode, or it may be used as part of theconsultation mode. In general, the consultation mode may display asubset of the array of treatment plans; the treatment plans included inthe subset may be selected by the user, or in some variations may beautomatically selected based, e.g., on known user preferences. Theseselected treatment plans may then be presented, using the consultationmode, to the subject. In FIG. 12, the consultation summary screen showstwo treatment plans 1201, 1203 as both images of the teeth (at theselected stage of treatment to be shown) and treatment details ortreatment preferences 1215 (e.g., allowing/not allowing IPR,allowing/not allowing attachments, etc.). The display may also show thetreatment concerns that are addressed by each treatment plan 1217 (e.g.,resolved upper and lower crowding, resolved open bite, etc.). This mayallow direct, including side-by-side, comparison by the patient. Thescreen in FIG. 12 also illustrates the patient information, includingname 1220 (“Joe Smith”), the initial positions of the teeth 1221, animage of the patient 1223, and an analysis of the initialmalocclusion(s) 1225. Controls on the display may allow the user toenter a consolation mode, in which a simplified display of the treatmentplans may corresponding to various treatments may be shown to thepatient.

FIG. 13, shows a “consultation mode” display screen, for display to apatient based on the subset of treatment plans selected by the user. InFIG. 13, the consultation mode screen shows two selected treatment plans1303, 1305, for comparison with the patient's current dentition 1301.The first treatment plan is a 26 stage plan 1303, while the secondtreatment plan is a 14 stage treatment plan in this example. Any subsetof treatment plans may be shown. In this example, the various treatmentplans are shown with annotation indicating how well they address thepatient's identified malocclusions 1307. For example, the 26 stagetreatment plan (which may correspond to a first product) resolves boththe upper and lower crowding and the open bite 1309. The 14 stagetreatment plan (which may correspond to a second product) resolves theupper and lower crowding, and partially resolves the open bite 1312.

From the consultation mode, the user and/or the patient may review, in asequential or side-by-side display, the various selected treatmentplans, and may select between them. The consultation mode may alsoinclude information about the cost and/or timing of the treatment plans(including the number of stages, etc.).

FIG. 14 is an example of a display for showing detail (includinganimation) for a particular treatment plan. Individual stages may beselected.

In general, patient information, including dental record information,may be shown as well. For example, as a reference, the methods andapparatuses may include a display of the patient's upper and lowerarches (e.g., see FIG. 15). In FIG. 15, the display shows images of theupper and lower jaw at two times (e.g., 2005 and 2011) for the patient.This type of display shows the progression of the malocclusion overtime. In FIG. 15, the malocclusion includes a slipped contact and mesialdrift.

As mentioned above, the array of treatment plans may typically includethree or more (more preferably 12 or greater) treatment plans. FIGS.16A-16M illustrate one example of an array of treatment plans for apatient. FIG. 12A shows an example of the patient's actual dentition,shown as a digital model. As discussed above, this model may begenerated from a direct digital scan of the patient's teeth, or from animpression. FIGS. 16B-16M illustrate 12 alternative treatment plansgenerated for the patient and combined into an array of treatment plansthat the user may select from or modify further. FIGS. 16B-16M arearranged as a grid, for convenience, and a model of the final toothpositions, following completion of the treatment plans, is shown. Theactual treatment plan may include an indicator of position and/ororientation of each tooth, as well as key frames describing how totranslate from the initial position (e.g., FIG. 16A) to a final position(FIGS. 16B-16M). In FIGS. 16B-16D, shown as the horizontal axis, each ofthe three treatment plans is shown having been calculated with thetreatment details or treatment preferences set to not allow attachmentsand not allow IPR. The figures also show the use of 26, 15 or 7 stages,respectively for FIGS. 16B-16D. FIGS. 16E-16G show a series of treatmentplans (again 26, 15 or 7 stages, respectively) for which the attachmentswere allowed, but not IPR. FIGS. 16H, 16I, and 16J (26, 15 or 7 stages,respectively), show examples of the final stages of treatment plans inwhich attachments were not allowed, but IPR was allowed. Finally, FIGS.16K, 16L, and 16M (26, 15 or 7 stages, respectively), show examples inwhich the treatment plans were generated allowing both attachments andIPR.

An alternative treatment plan display and modification screen is shownin FIG. 17. In this example, the treatment plan is a 26 stage plan. Theinitial display is the 26 stage device which did not allow either IPR orattachments. In FIG. 17, the right half of the screen shows controls,configured as filters that may be selected to toggle between thedifferent treatment plans. Because the treatment plans are allpre-calculated and included it the array of treatment plans, they may beeasily and quickly toggled between each other, even in very large orcomplex treatment plans. FIG. 17 shows controls that allow the displayto switch between a treatment plan allowing IPR/not allowing IPR 1703,and treatment plans that allow or do not allow attachments 1705.Additional other controls may allow the user to toggle between differentproducts having different treatment durations (stages) 1707. In FIG. 17,the apparatus may also allow the user to select different treatmentdetails 1709.

Treatment Plan Optimizing Generator

Also described herein are the methods and apparatuses for automaticallycreating a treatment plan to align a patient's teeth using a pluralityof removable aligners to be worn in sequential stages. These methods andapparatuses may include creating a plurality of variations of treatmentplans to align a patient's teeth using a plurality of removable alignersto be worn in sequential stages. The method may be referred to herein asa method for automatically generating optimized treatment plans, and theapparatus (e.g., software, including non-transient, computer-readablemedium containing program instructions for creating a treatment plan toalign a patient's teeth using a plurality of removable aligners) may bereferred to as a treatment plan optimizing generator.

The methods for automatically generating optimized treatment plansdescribed herein may simultaneously optimize final position andintermediate teeth positions (e.g., staging). This may allow theapparatus to produce treatment plans having a final position that isachievable in exactly the allowed number of stages (and thereforeduration of treatment) for a product corresponding to a set number (orrange) of aligners.

The comprehensive treatment plans built using the methods ofautomatically generating optimized treatment plans described herein alsoincorporate an optimized or idealized treatment plan (which is referredto herein as a comprehensive treatment plan) generated withoutconsideration of the amount of time or number of stages it may take toachieve. This may enable the method to improve orthodontic measurementsthat are not explicitly defined as optimization goals. Measurements thatrepresent potential orthodontic problems may be restricted to a rangebetween the initial positions (or values) of the patient's teeth and thepositions (or values) planned in the comprehensive treatment. Thisensures that partial final position does not introduce or worsenorthodontic problems unnecessarily.

As an alternative to the methods and apparatuses described herein, atreatment plan may be created by first building (manually orautomatically or a combination of manually and automatically) thecomprehensive treatment plan, and then segmenting the plan into a seriesof movement-limited stages. In this method, the number of stages dependsupon the final positions of the teeth. Stages are determined by, e.g.,iteratively simplifying the leading tooth movements. FIG. 18 shows oneexample of a process flow for this method, in which the initial positionof the teeth is provided along with the user (e.g., dentalprofessional's) prescription and preferences as inputs to generate thefinal portion of the teeth (e.g., the comprehensive treatment plan). Thefinal position produced by this method may not always satisfy productconstraints due to inaccuracy of treatment length estimation. Further,straight-forward simplification of tooth movements that may be requiredto segment the steps of the plan may unnecessarily compromises qualityof the final position. Finally, treatment plan may not prioritizeaesthetic goals over orthodontic norms and rules, achieving sub-optimalresolution of the likely patient's chief concerns. Although theseproblems may be mitigated by personal judgement of technicians, suchmanual adjustments may take significant time and the produced plans maylack consistent quality.

The method in FIG. 18, which involves sequentially solving for acomprehensive final position (“final position generation”), thensegmenting this into a series of aligners (“staging generation”) andfinally outputting the treatment plan including both the final positionand staging (“output”) is a linear process, although it may includeiteration to adjust the final position and/or staging. As mentionedabove, there are often situation in which it is desirable to pan atreatment in which the parameters such as the length of treatment areconstrained. Further, it would be beneficial to provide methods andapparatuses for treatment planning in which the entire treatment plan(e.g., each stage) is determined at the same time, rather thansequentially.

Described herein are methods and apparatuses for generating orthodontictreatment plans by expressing the target treatment goals for toothmovement as numerical expressions and limiting these target treatmentgoals by numeric constraints corresponding to limits on the treatment.Once the treatment goals and limitations are defined numerically, theresulting numeric expression (e.g., equations) may be treated as anon-linear optimization problem and solved to generate an optimaltreatment plan given the constraints and target goals. These method mayresult in generating treatment plans that may be referred to as “partialplans” because they are not intended to fully resolve all of thepatient's clinical orthodontic conditions, but may best resolve themwithin the given product limits (e.g., within a limited treatmenttime/number of stages, etc.).

FIG. 19 schematically illustrates a simplified overview of the conceptunderlying the method for automatically generating optimized treatmentplans described herein. In FIG. 19, the region within the circle 1903represents all of the treatment plans and final positions that may beachieved from a patient's starting tooth configuration (shown as thecentral circle 1905, in the upper left). The circle therefore containsall of the final tooth positions and treatment plans for achieving thesefinal positions when the treatment plan is constrained by the limits ofthe aligner system (e.g., the limits on the number of stages, the limitson the amount and rate of movement of each tooth, etc.) and the limitsrequired by the dental professional (e.g., restricting movement of someteeth, etc.). These limits may be referred to as the treatmentpreferences and the treatment details. The circle shown in FIG. 19 ishighly simplified; the space bounded by the constraints may bemulti-dimensional, but the principle concept is the same as shown inFIG. 19.

A comprehensive treatment plan is typically determined without concernfor all or most of the constraints forming the boundary 1903. Thus, inFIG. 19, the comprehensive treatment plan (“ideal final”) 1907 is shownlocated outside of the space formed by the boundary 1903, although intheory it may be inside or outside. An image of the final tooth positioncorresponding to the comprehensive treatment plan is shown in the bottomright of FIG. 19. Since this orthodontically ideal final position maynot be achievable within the boundary, the space contained within theboundary must be examined to identify the next-best treatment plan thatsatisfies as many of the treatment concerns while providing anaesthetically pleasing result.

One possible solution may be to find the treatment plan within theboundary that is close to the ideal final position. In FIG. 19, theclosest position 1909 results in a final position of the teeth that isunsatisfactory. As shown in the upper right corner of FIG. 19, thetreatment plan that is closest to the ideal final position within theboundary is does not resolve the principle concern (e.g., crowding)though it may address other concerns (e.g., leveling, etc.), and insteadcreates or makes worse other problems, such as spacing of the teeth.Although almost all of the teeth, except one, achieved a final positionnearly identical to the ideal final position, the resulting finalposition is both orthodontically and aesthetically unsatisfactory.

Instead, the optimal position 1911 that both resolves the principleconcern (e.g., crowding of the teeth) and results in an aestheticallypleasing result is shown in the bottom left of FIG. 19. Although fewerteeth achieved the final position that is the same as the optimalposition, the resulting final position is superior to the closestposition shown.

In practice, the ideal fit may be found by expressing the constraints asa numeric expressions and a set of limits on these numeric expressionand solving the resulting expression as an optimization problem.Specifically, the method may include identifying, for a particularpatient, a set of treatment preferences and treatment details,expressing these treatment preferences and treatment constrains as anonlinear expression, and solving the optimization problem. FIG. 20Aillustrate a schematic of this method. In FIG. 20A, the input into themethod (or an apparatus performing the method) is the initial positionof the patient's teeth, the dental professional's prescription andpreferences, and the definition of the product. The definition of theproduct may be thought of as the set of treatment preferences. This mayinclude, for example, the number of stages, the properties of thealigners including the rate of movement of the teeth by the aligner,etc. The user's prescription and preferences may correspond to thetreatment details.

In any of the methods and apparatuses described herein, it may bebeneficial to have an ideal tooth position (e.g., the comprehensivefinal tooth position) for use in the treatment planning. However, itshould be clear that this comprehensive final tooth position is not usedas the actual final tooth position. Instead, the methods describedherein concurrently determine both the actual final tooth position andthe stages required to achieve that tooth position within the limitsrequired by the treatment preferences and treatment details. Softwarefor determining a comprehensive final position may be used (which mayalso be referred to as “FiPos” software) or the final position may bemanually, or semi-manually/semi-automatically determined eitherdigitally or manually (e.g., using a model of the patient's teeth) anddigitized.

Once a comprehensive final tooth position has been identified (“FullFinal Position Generation”), this final position may be used, along withthe initial position, treatment preferences and treatment details, todetermine the optimal treatment plan, using “optimization treatmentplanning.” This optimized treatment planning is described in greaterdetail below. The optimization treatment planning may include result ina vector description including the staging, key frames (showing movementof the teeth between stages) and a proposed final position of the teeth,which may be output (“output”) by the system.

FIG. 20B illustrates this method is slightly more detail, showing therules and problems to be solved for the determination of thecomprehensive final position, as well as an example of the rules andlimitations for determining an optimization problem that can be solvedfor an optimized treatment plan.

In FIG. 20C, the same four inputs (product definition/treatment details2003, preferences (treatment preferences, user-specific and/or patientspecific) 2005, initial tooth position 2007, and comprehensive toothposition 2009) are used by the treatment plan optimizing generator toselect a plurality of numerically expressed treatment targets from amemory accessible to the processor 2011. The memory may generallyinclude a set of pre-defined generic expression (“merit functions” ormerit function components, or “target functions”) that describe thenumerically expressed treatment targets. Typically each of these targetsis a numeric function that has a value that is closest to zero for idealcases. For example, as will be described below, if the treatment targetis alignment in an x direction, the numeric function may express thedeviation from alignment in the x direction as a numeric vale (e.g.,from 0, meaning in alignment, to some distance, e.g., in mm, out ofalignment).

Similarly, the treatment preferences may be expressed as limits on thetarget functions. The treatment preferences, and in some variationstreatment details, initial positions and comprehensive positions may beused to select the numeric limits from a stored set of pre-definedgeneric constraints. Once the numeric limits and target functions havebeen selected (e.g., based on the set of treatment details, the set oftreatment preferences and the comprehensive final position of thepatient's teeth) 2015, resulting in the specialized constraints (limits)2017 and specialized numerically expressed treatment targets (targetfunctions) 2019, they may be expressed as a non-linear optimizationproblem 2021 by first combining the plurality of numerically expressedtreatment targets (target functions) to form a single numerical function(single numerical merit function). Each numerically expressed treatmenttarget may be multiplied by a scaling factor. The resulting non-linearoptimization problem is a single numerical function subject to theplurality of numeric limits 2023.

Thereafter, the optimization problem may be solved using conventionaltechniques, such as an interior point method. Such nonlinear constrainedoptimization solution techniques 2025 may minimize the single numericalfunction subject to the plurality of numeric limits to get a solutionvector including all stages forming the treatment plan 2027. Thesolution vector may be mapped to a treatment plan 2029, wherein this“optimized” treatment plan 2033 includes a final tooth position that isdifferent from the comprehensive final position of the patient's teeth.

An optimized treatment plan may be identified by solving an optimizationproblem once the constraints on the patient's teeth (e.g., productdefinition/treatment details and treatment preferences) are expressed asnumeric functions and limits. Non-linear constrained optimizationproblems can be represented by a merit function and a set of inequalityconstraints:

$\begin{matrix}{minimize} & {f_{0}(x)} & \; \\{{subject}\mspace{14mu}{to}} & {{{f_{i}(x)} \leq 0},} & {{i = 1},\ldots\mspace{14mu},m,} \\\; & {{x_{j}^{\min} \leq x_{j} \leq x_{j}^{\max}},} & {{j = 1},\ldots\mspace{14mu},{n.}}\end{matrix}$

See, e.g., FIG. 21. To produce treatment plan by solving optimizationproblem, the treatment plan is described in terms of distinct values,which are mapped to x_(j) variables in the problem statement. Onepossible mapping, used in the first implementation of the method, isdescribed below. The position of each tooth at the final stage isdescribed in terms of six coordinates (orientation, e.g., rotation, andtranslation from the center of the jaw) and mapped to six variables.Staging, i.e. intermediate positions, of each tooth is described as alinear combination of several functional component. Each componentdescribes deviation from linear movement at a certain stage and isparametrized by six coordinate deviations and a stage number. Thus, eachfunctional component is mapped to seven variables in optimization space,per tooth.

The numeric limits on the single numerical function are understood to bequalities of treatment plan that must never be violated and may bedefined as inequality constraints Constraints enforce mechanical,biomechanical, clinical and aesthetic rules, as well limits imposed byproduct definitions. Implemented constraints include, but are notlimited to, amount of reproximation, maximum velocity of tooth movement,depth of inter-arch collisions, cusp-to-groove occlusion. Example ofconstrains also include “do-no-harm” constrains that ensure that themovement of the teeth does not result in making the alignment worse orovercorrecting, e.g.: midline, overjet, overbite, occlusion,misalignment, spaces, rotations, etc. Other constraints may include:amount of collisions, movement velocities and separation of movements,etc.

Qualities of treatment plan that must be improved as much as possiblewithin constraints are defined as numerically expressed treatmenttargets, i.e. components of merit function, ƒ₀. Targets are typicallyfeatures that are to be improved or modified by the treatment. Targetsmay include, but are not limited to, length of the resulting treatment,amount of spaces, misalignment between teeth, etc. For example,potential chief concerns may include: misalignment (x and z),de-rotation, occlusion, diastema and spaces, inter-arch collisions, etc.Other targets may include: closeness to comprehensive setup, androundtrips. The merit function(s) are defined as a non-linearcombination of target functions, weighted by pre-defined coefficients.All of the target functions may be summed (and weighted) to form asingle numerical function (single numerical merit function).

For example, target functions that may be weighted, summed and minimizedas described herein may include: minimal difference with ideal finalposition (with the target of trying to achieve an ideal final position);misalignment, e.g., by minimizing the difference between x- andz-misalignment in value final position and in ideal one; tooth toaligned to arch (e.g., minimize the angle between the x axis in a valuefinal position and an ideal one); minimal diastema (e.g., minimizespaces between neighboring teeth); occlusion (e.g., applicable for caseswith both jaws, pull corresponding cusps from one jaw to the groves fromopposite jaw); round-trip (e.g., minimize mesial-distal and buccallingual round-trips); inter-arch collisions in value position(applicable only for cases with both jaws, e.g., try to createinter-arch collision at posterior teeth as close to ideal final positionas possible); inter-arch collisions during staging, etc.

In general, measurement may be a function implemented in software thatcan be used as target or constraint in the optimization problem. Theinput for every measurement may be: 3D models of all teeth (constants),six coordinates per tooth that define the tooth position relative to thejaw. The output of every measurement may be a single numerical value,such as distance in mm, angle in radians, or score from 0 to 5.

Examples of targets are shown in FIGS. 22A-25 illustrate examples oftargets and constrains that are expressed as numeric functions andlimits. For example, FIG. 22A shows one method of quantifying occlusion(e.g., between upper and lower jaws). In FIG. 22A, the occlusion metricis the cumulative distance between all corresponding cusp points fromone jaw and groove spline from opposite jaw. For the upper jaw, lingualcusps are used and for the lower jaw, buccal cusps are used. Thus, thequality of the occlusion is measured as a function of distances betweenoccluding grooves and cusps. The constraints of the optimization problemmay ensure that quality of occlusion in partial setup is not worse thanthe patient's initial position. As a result, if the patient's cross bitecannot be fully fixed with good occlusion in low-stage product, it willnot be corrected. This is illustrated in FIGS. 22B-22D. FIG. 22B shows aview of a patient's initial tooth configuration (cross bite). FIG. 22Cshows the correction using a comprehensive final position to correct.FIG. 22D shows a comparable correction using a ‘partial’ optimizationsetup as described herein.

FIG. 23 shows an example of the quantification of x-misalignment.X-misalignment is a projection of a line between buccal ridge end pointsof two neighbor teeth onto the arch normal in a given stage 2303 (yellowline). Similarly, FIG. 24 illustrates quantification of z-misalignment.Z-Misalignment is a projection of a difference of tooth tip point ontothe jaw occlusal plane's normal in a given stage 2403.

FIG. 25 illustrates alignment to arch quantification. As illustrated,alignment to arch for a given tooth is the angle between a projection ofX axis in a value final position and an ideal one.

Examples of constraints include tooth movement limits that typicallyrequire that the range of movements that are allowed are limited forevery dental type according the product definition. These limits may bedefined clinically to ensure that the proposed treatment plans areachievable in practice with the device to be used. Each product (e.g.,aligner) may different set of values, which may be stored in a look-uptable or other memory accessible by the processor.

Tooth movement limits may include rotation (e.g., tooth rotation along zaxis); tip (e.g., tooth rotation along x axis), torque (e.g., toothrotation along y axis); crown movement, including horizontal crownmovement (e.g., translation along z axis ignored), buccal-lingual crownmovement (crown center translation along x axis), mesial-distal crownmovement (e.g., crown center translation along y axis); mesial-distalroot apex movement (e.g., root apex translation along y axis);buccal-lingual root apex movement (e.g., root apex translation along xaxis); extrusion/intrusion (e.g., tooth translation along z axis); andrelative extrusion.

Collision constraints may also be used to limit collisions betweenteeth. Further, staging constraints may be applied to intermediatestages (e.g., key frames) to ensure that the treatment is plan isconsistent and clinically predictable. Collision constraints may includeinter arch collision (applicable only for cases with both jaws), whichforbids deep collisions greater than, e.g., 0.05 mm in depth, on theposterior teeth and may forbid smaller or equal depth in anterior teethin the value final position. Collision constrains may also forbid onearch collision (e.g., so that collision between neighbor teeth in valuefinal position does not exceed a maximum of collisions in initial, idealfinal or value corresponding to the tight contact).

Staging constraints may also be used. For example, stating constraintsmay include synchronized finish of value final positions (e.g., everytooth must complete movement at the same stage number); fixed stageconstraints (e.g., every tooth starts movement at stage 0); “not greaterstage” (e.g., the final stage number, treatment length, must not begreater than allowed in the product (i.e. 20 stages, etc.); a “do nottrigger Stairs pattern” (e.g., do not exceed mesial-distal movements onevery tooth that can be predictably achieved in practice without longsequential teeth movements, referred to as a stairs pattern);constraints so that no Z-rotation and Intrusion/Extrusion round-tripsoccur on any tooth; and velocity rules (e.g., tooth movement over asingle stage, e.g., aligner, must not exceed 0.25 mm).

Other examples of constraints include “do no harm” constraints, whichensure that planned final position does not introduce or worsenorthodontic problems. In the optimized final position, the value ofevery measurement that corresponds to an orthodontic condition must liewithin the value measured in initial position, and the value measured inthe comprehensive (ideal) final position. For example, overjet may belimited (applicable only for cases with both jaws) by requiring thateach jaw should have at least one incisor for each side. Overbite may belimited (applicable only for cases with both jaws); each jaw should haveat least one incisor for each side. Midline may be limited (applicableonly for cases with both jaws); each jaw should have more than twoanteriors. Occlusion may be limited (applicable only for cases with bothjaws). X- and z-misalignment may be limited (applicable for each pair ofneighbor teeth where at least one tooth is movable); arch and jawocclusal plane may be calculated once in initial position. Spacing(applicable for each pair of neighbor teeth where at least one tooth ismovable) may be limited; crown space between neighbor teeth should notexceed maximum of spaces in initial and ideal final positions. Angularmay be limited by keeping teeth axes between initial and ideal finalposition (alignment to arch measurement for x, y and z axes).

Once the problem is stated in this manner it can be solved by anyconstrained optimization algorithm of sufficient power, such as anInterior Point method. The result is a solution vector. The vector willinclude position and orientation values for each tooth, as well as stagenumber corresponding to each tooth. The vector may describe a largenumber of such values, e.g., x_(j) variables.

The produced solution vector of optimal values of x_(j) variables may beconverted to the treatment plan by the mapping of variables describedabove in reference to FIG. 20C.

In general, these methods may be used to generate partial treatmentplans that are characterized by addressing patient's concerns as much aspossible within the product limits. In contrast to comprehensive, orfull, treatment plans that have as their end point the ideal,comprehensive tooth position, these partial treatment plans may notfully resolve all of the concerns of the dental professional, and maynot address all orthodontic problems. To produce such partial plan,treatment length and tooth limits allowed within the product areimplemented as inequality constraints. This forces the optimizationalgorithm to find a solution, i.e. treatment plan, within the productlimits, that improves merit function as much as possible, but not to thefull degree.

In general, to improve quality of the plans, an optimization target(e.g., the comprehensive tooth position) may be added to minimizedistance between the partial plan and the comprehensive treatment. Thisdistance can be measured by a length of secondary treatment thatachieves comprehensive final position starting from the partial finalposition. Full final position for the comprehensive treatment plan maybe produced manually, automatically or semi-automatically, as mentionedabove, and is stored separately in apparatus. Once the partial treatmentplan is ready, full final position is discarded.

To ensure that the partial treatment plans generated as described herein(optimized treatment plans) do not introduce or worsen orthodonticproblems, additional inequality constraints may be introduced. Asdiscussed above, each identified orthodontic problem, such as deep biteor class, may be measured as a single numerical value. Next, twoinequalities constrain such measurement in partial setup to the rangebetween the initial value and the comprehensive treatment. Formerinequality ensures that partial setup does not worsen the problem overthe initial position. The second (optional) inequality may ensure thatpartial setup does not overcorrect the problem unnecessarily.

By including a comprehensive final position, and incorporating it themerit function and constraints of the non-linear optimization problem,and solving this problem using the generic optimization algorithms, themethod described herein may produce treatment plans that fully satisfythe constrains from the product and user preferences, while optimallyresolving chief concerns, improving and maintain other orthodonticmeasurements.

The methods described herein can be straight-forwardly applied to allproducts with limits on number of stages or amount of tooth movement. Bybuilding such plans automatically, they may enable a dental professionalto review multiple plans for a product range, or customize product whilereviewing the updated treatment plan, as described above. Restriction onthe number of stages may be replaced or supplemented with otherrestrictions and goals; this may allow the method to incorporate chiefconcerns, doctor's preferences and predictability models intocomprehensive treatment plans as well.

The methods and apparatuses described herein are also fully compatiblewith the use of biomechanical solutions that can potentially be combinedwith optimization of final and intermediate tooth positions to producetreatment plans with movements that are fully supported by the appliance(e.g., aligner) design.

Collision Detection

Construction of orthodontic treatment for a patient must account forlimitations on mutual position of teeth, including amount of space andinterproximal reduction. Computing exact amount of collisions and spacesbetween teeth may be a computationally intensive operation that impactscost and quality of automatic treatment plans. Described herein aremethods and apparatuses (e.g., such as system for automaticallydetecting collisions between teeth, which may be referred to ascollision detectors) for constructing approximated shapes of teeth bypacking the surface(s) of the teeth, or in some variations, otherstructures (e.g., attachments, brackets, etc.) using multiple threedimensional (3D) shapes (such as capsules) having a planar figure (e.g.,line, rectangle, etc.) in the core, and an outer surface extending aconstant radius from the core in x, y and z. Collisions (e.g., overlap)between the teeth may be analytically determined from the 3D shapes withhigh precision. These systems and methods may also be applied to justadjacent portion of the teeth (rather than the entire teeth) and may becombined with a hierarchy of bounding boxes in order to accelerate thecomputation. Compared to precise generic technique or estimatingcollision, these methods and apparatuses described herein may be two ormore orders of magnitude faster, and may allow the systems and methodsdescribed above for calculating one or more treatment plans (e.g., asolver or a treatment plan solver) to incorporate these collisiondetectors. Furthermore, any of the methods and apparatuses describedherein may determine both the magnitude of the overlap (or in somecases, the closest separation) between the teeth, but may also beconfigured to determine the velocity of the overlap (e.g., in three ormore spatial directions, such as x, y, z and/or yaw, pitch, roll).

FIG. 29A illustrates the use of a triangular mesh 2905 to model thesurface of a shape, such as a tooth. Surface modeling using a triangularmesh may be used to model adjacent teeth and the modeled surface may beused to estimate the distance between objects such as teeth. FIG. 29Bshows an example of a group of three-dimensional (3D) shapes, shown ascapsules, in which the 3D shapes each have a core that is a line or aplane figure and an outer surface that is a constant radius from thecore. In FIG. 29B the capsules 2907 are formed by a core that is a line.As will be described in greater detail below, modeling the surfaces ofadjacent teeth by packing these surfaces (and internal regions) withcapsules as described herein may be used to determine collisions betweenthe shapes much more rapidly than other methods, including modeling bytriangular mesh, as shown in FIG. 29A. For example, a tooth surface maybe modeled with high precision using 2000-8000 triangles; the samesurface may be modeled using 50-200 capsules with nearly equivalentprecision. Because the capsules have both flat and convex regions theymay be particularly well suited to modeling shapes such as the surfaceof a tooth. Using 3D shapes having a constant radius from a planar shape(e.g., line, rectangle, etc.) may be used to calculate the distancebetween the surfaces more than five times faster compared to modelingwith triangles at an equivalent precision. The 3D shapes, such ascapsules, are typically solids, and may therefore be used for fastpenetration depth computation.

FIG. 29C shows a side-by-side comparison of a tooth modeled with bothcapsules 2917 (entire tooth) and triangular mesh (right side 2915). Inpractice, the patient's teeth only need to be modeled by packing withthree dimensional shapes such as capsules once; thereafter the overalltooth position may be changed, but the same surface modeled by the 3Dshapes may be used to examine collisions/spacing for multiple differentarrangements of the teeth.

Any appropriate 3D shape having a core that and an outer surface that isa constant radius from the core may be used, although it has been foundthat using shapes with at least partially linear cores (e.g., capsules,rounded rectangles, etc.) may be particularly beneficial for modelingthe tooth surfaces and estimating distanced, including collisions, anddepths of collision. For example, FIGS. 30A-30C show sections through 3Dshapes having a core and an outer surface that is a constant radius fromthe core are shown; the corresponding figures shown are shown inperspective view in FIGS. 31A-31C. In FIGS. 30A and 31A the shape is asphere having a core 3001 that is a point at which the radius, r, 3003originates. The use of a sphere, which has only a concave outer surface,for packing a complex shape such as the tooth surface may be suboptimal,in part because the surface of the tooth includes regions that are notconcave. The use of spheres may require a larger number of smallerspheres for packing to approximate the tooth surface compared to othershapes such as capsules like those shown in FIGS. 30B and 31B. In FIGS.30B and 31B, the capsule has core that is a line segment 3005, and anouter surface that is a constant radius, r, 3007 on all side of the linein x, y and z space. Similarly, FIGS. 30C and 31C show an example inwhich the core is a closed planer shape, shown as a rectangle 3009having a constant-length radius 3011 extending from the surface. Theouter surfaces are shown in the perspective views of FIGS. 31A-31C.

When modeling the tooth using the 3D shapes such as capsules, a varietyof different capsule sizes may be used; the capsules may have differentlengths of the core line segment, and/or the radius of each capsuleextending from the core may be different (though typically the sameradius length in an individual capsule). Alternative or additionally,different 3D shapes may be used.

FIGS. 32A and 32B illustrate top and side perspective views,respectively, of a patient's molar 3201 that has been modeled using aplurality of capsules. In this example, the entire outer surface of theportion of the tooth above the gingiva has been modeled by packing withcapsules. In practice one or more teeth may be modeled from a digitalmodel of the patient's tooth or teeth. For example, a digital scan ofthe patient's teeth (e.g., from an intraoral scan, a scan of animpression of the teeth, etc.) may be provided and the surface of theteeth may be modeled by packing the tooth surface (and all or theperipheral region of the tooth volume) with a plurality of 3D shapes,such as capsules. An optimization algorithm may be used to automaticallyposition a small number of capsules to approximate the tooth surface asclose as possible. The precision of the match with the tooth surface maybe set as a parameter, so that the minimum number of capsules (ormaximum size of capsules) necessary to model the surface within the setprecision may be determined.

In variations in which the patient's teeth are digitally scanned, thedigital scan may be segmented into individual teeth (or groups of teeth)and each segmented region, e.g., tooth, may be modeled with 3D shapes(e.g., capsules). In some variations the tooth or teeth may already bemodeled in another manner (e.g., by triangles as described in FIG. 29A)and the existing model may be modeled with the 3D shapes.

To model an individual tooth (or group of teeth), the tooth may bepacked with capsules so that difference between tooth's surface and theouter surface of the capsules is as low as possible. In this model, onlythe 3D shapes, e.g., capsules, are used for approximations; these 3Dshapes may be constructed quickly and may be analyzed quickly. As willbe described in greater detail below, in some variations, only a part ofa tooth may be approximated. For example, only the IP area, incisalarea, crown, etc. may be modeled; for example, only the side of thetooth facing the adjacent tooth may be modeled. Alternatively, the wholetooth shape may be modeled. In some variations, the tooth shape may bedecimated before approximating. For example, the tooth shape may besimplified by filtering (e.g., smoothing, etc.). Alternatively oradditionally, the original shape can be used to obtain more preciseapproximations. In some variations, all of the teeth (or subsets ofteeth) can be modeled simultaneously, e.g., in parallel. Alternatively,teeth may be modeled one-by-one, e.g., sequentially.

Modeling the tooth may be iterative. The surface may initially be filledwith non-overlapping 3D shapes (e.g., capsules) as a startingconfiguration. Each iteration may include: finding the area of shapewhich is approximated by capsules the worst (e.g., comparing the digitaltooth surface, or “actual surface,” to the 3D shape-filled surface). Onoptimization problem may be constructed for approximating this area with1 capsule object. For example, the following relationship may beminimized, subject to the constraints that the end points of eachcapsule must lie inside of the convex hull of the tooth shape, and eachleast square straight-line (LSS) closet vertex from the tooth shapeshould not be farther than some small limit:

$\sum\limits_{k}\left\lbrack {\omega_{k\mspace{11mu}}{\min\limits_{m}\mspace{11mu}{{Distance}\mspace{14mu}\left( {{vertex}_{k},{capsule}_{m}} \right)}}} \right\rbrack^{2}$

In this relationship, w_(k) is the weight for vertex v_(k) of theoriginal shape. For interproximal (IP, the region between adjacentteeth) area approximations:

ω_(k) =f({vertex_(k)}_(y) ²⁾

This may be solved with an optimization solver, and a newly foundsurface may be added to the approximation, while obsolete surfaces maybe removed from the approximation. The total approximation may then berefined. This process may be repeated (iterated) as much as necessaryuntil the desired precision is achieved.

For example, in some variations, the systems and methods describedherein may select a subset of vertices from the digital model (e.g.,scan) of the tooth surface, and may approximate this subset of verticeswith one capsule. An optimization solver may be used to minimize thedistance between the capsule and the selected subset of points. If theapproximation is poor (e.g., below some threshold for approximation),the set of point is not adequate, and the subset of vertices may berevised to find points within the vertices that may be approximatedbetter, or finding new sets of points that may be approximated moreclosely within the desired range (e.g., another capsule may beidentified to approximate the smaller subset of points). Once theinitial packing of capsules has been completed, each approximating asmall subset of points on the tooth, the optimization process may berepeated with some of the capsules rearranged to achieve a higherprecisions. The process may stop when the maximum amount of capsulesdesired is reached. For example, the threshold number of capsules may beset to, e.g., 15 capsules (10 capsules, 12 capsules, 15 capsules, 20capsules, 25 capsules, 30 capsules, 35 capsules, etc.). Alternatively,in some variations, the process may be repeated until a precision limitor threshold is reached, without limiting the number (and thereforesize) of capsules. For example, a precision limit may be set to requirefilling of all spaces bigger than 0.001 mm. Alternatively, a combinationor balance of the two (number of capsules and/or minimum precisionlimit) may be used, for example, increasing the number of capsules ifthe precision is within a predefined range.

Although FIG. 32A-32B illustrates an example of an entire tooth modeledusing a plurality of capsules, other structures may also be modeled,including other dental structures that may be present on the tooth orassociated with the tooth. For example, FIGS. 33A-33B illustrateperspective views of a portion of a dental appliance (a precision wingportion 3301) that has been modeled by packing with a plurality of 3Dshapes (e.g. capsules). In some variations, this may be beneficial fordetecting collision between the teeth and an orthodontic device, orbetween multiple orthodontic devices, etc.

FIG. 34A illustrates an example of a tooth having a surface (aninterproximal surface) that is modeled using a plurality of capsules. InFIG. 34A, the left interproximal surface 3405 is approximated by packingthe surface with a plurality of capsules of various sizes. Other regionof the tooth (e.g. crown region) are not modeled, or not modeled to thesimilar precision. In some variations, multiple regions associated withthe same tooth may be modeled separately, such as left and rightinterproximal regions, crown regions, etc. FIG. 34B illustrates a dentalarch including a plurality of individual teeth. Each tooth is divided upinto left and right sides, and in some teeth (e.g., molars, premolars) aseparate middle region; the left and right regions may be modeledseparately. For example, the boxed incisor 3408 includes a left side3410 and a right side 3412, shown by different shading, and similardistinctions can be made for all of the teeth.

Once one or more surfaces of the teeth have been digitally modeled bypacking 3D shapes, a hierarchy of bounding boxes may be formed aroundall of the 3D shapes and adjacent sets of shapes for each modeledsurface of each tooth. Building a hierarchy of bounding boxes mayprovide a rapid and efficient way to determine which capsules betweentwo adjacent teeth may be closest to each other and/or may overlap. Theuse of bounding boxes, and particularly an organized hierarchy ofbounding boxes, may reduce the time for finding closest pair of capsulesdramatically. The bounding boxes allow the rapid determination of anapproximate value of a collision/separation in space, instead of aprecise one. The approximate value may be calculated as a minimaldistance between all possible pairs of capsules of two shapes. Forexample, approximate collisions can be used in optimization process oftreatment plan generation to provide a good initial guess of teethposition that fulfills almost all requirements besides some smallviolations of collision/space rules left due to imprecision ofapproximate calculations. Those violations can be resolved by switchingback to precise calculations (e.g., using the capsule distance). Thiscombination of bounding boxes and 3D shapes, allowing both rough andmore precise determination of spacing, has been found to give asubstantial performance boost of up to 150 or more times compared to theuse of more precise collision depth/space calculations only.

The use of the hierarchy of bounding boxes, which provide approximatecollision information, with the more precise collision informationprovided by the 3D shapes, such as capsules, particularly by increasingthe number of capsules, may allow both rapid and accuratecollision/spacing information.

The hierarchy of bounding boxes may be organized so that each capsule isput into a bounding box that fits it tightly. Each bounding boxcontaining one or more capsules are considered leafs of the hierarchy.Each box from a higher level of hierarchy bounds several boxes from alower level of hierarchy. FIG. 35A illustrates one example of ahierarchy of bounding boxes for four capsules. In this example, capsulesA, B, C, D are each bound in a bounding box, forming the lowest level ofthe hierarchy. Bounding boxes A and B are united into bounding box AB,and bounding boxes C and D are united into bounding box CD. Finally, atthe top of the hierarchy, bounding boxes AB and CD are united inbounding box ABCD. FIG. 35A shows the entire hierarchy arranged as atree, with the boxes corresponding to individual capsules at the lowestlevel.

Any appropriate algorithm for construction of a hierarchy of boundingboxes can be used. Using tighter bounding boxes (e.g., having smallervolumes) may result in more efficient usage of the hierarchy incollisions computations, therefore the methods and apparatuses describedherein may build a hierarchy while minimizing the volume of theresulting bounding boxes on each level of hierarchy. Each tooth may havea single hierarchy, or multiple hierarchies, e.g., corresponding to theleft interproximal side and the right interproximal sides, etc. Thehierarchy may be traversed to avoid calculation of distances betweenpairs of capsules that cannot influence the outcome value ofcollision/space when checking adjacent teeth for collisions. Forexample, FIG. 36 illustrates an example of a method (e.g., shown here aspseudo-code) for traversal of bounding box hierarchies to skip distancecalculation between capsules that cannot influence the final value ofcollision/space. This method may start at the highest level and see ifthere is any collision (e.g., overlap) between the highest levels of thehierarchy by, e.g., measuring the distances between the largest (toplevel) bounding box for each adjacent tooth or both adjacent toothregions. If there is no overlap at the top level, there is no collisionat all. However, if there is a collision, then the next level down thehierarchy may be compared to determine which branches of the hierarchyinclude collisions; for each branch that includes a collision, theprocedure may continue down to the next level/branch until the lowestlevel (capsule or other 3D shape) is reached; the final levels on bothteeth, or regions of the teeth, therefore represent the regions that arecolliding, and these regions may be examined to determine the depth(magnitude) of collision. FIG. 37A illustrates one method ofanalytically determining the distance between two capsules of differenthierarchies. In general, the apparatuses and methods may measure thedistance, d, between the cores of the 3D shapes and the minimumseparation between the capsules in this example is equivalent to theshortest distance between the two line segments minus the radius of thefirst capsule and the radius of the second capsule. FIG. 37B alsoincludes an example of a pseudo-code set of instructions for findingapproximate distance between two shapes, such as, for example, shape Aand shape B packed with capsules shown in FIGS. 35A-35B. Although theexamples described herein include bounding boxes, other simplifiedbounding geometries may be used, for example, bounding sphere orbounding capsule hierarchies may be used.

In addition to detecting the magnitude of any collision that occurs whenthe teeth are in a specified position, the methods and apparatusesdescribed herein may be used to determine the velocity of any collision.In doing velocity measurements, one or both teeth may be moved verysmall increments (e.g., less than 0.001 mm, less than 0.01 mm, etc.) inone or more axis (x, y, z axis, roll, pitch and yaw), and the resultingchange in the overlap determined for each axis. The final velocity maybe measured for each of the six axes, and/or may be combined into asingle indicator (e.g., vector) sum or relationship.

During any of the processes for determining the velocity of a collision,in which the tooth may be ‘jittered’ in one or more of its axes, theclosest pair of capsules in collision/space with any change in positionof shape is very small. This can be used for faster calculation ofgradients in optimization algorithm for determining the final positionof the teeth following treatment, and for staging construction. Forexample, the tooth may be moved in each of the six axes (e.g., threetranslational axes, x, y and z, and three rotational axes: pitch, yawand roll) by a small amount (e.g., less than 0.001 mm of translation,less than 0.01 degree of rotation, etc.). This is illustrated in FIG.40, for example, showing the axes around one tooth. The same capsulesidentified as colliding may therefore be re-examined following the smallmovements to determine the velocity of the collision. When using thesolver/engine to solve for one or more treatment plan, the solver mayavoid collisions between teeth. For the solver to estimate an optimalsolution when planning a treatment, the solver may be provided by notjust the magnitude (e.g., depth) of the collision, but also the velocityof the collision, e.g., how the collision depth reacts to small changesof position relative to the neighboring tooth. If one tooth is fixed,but the other is moved, e.g., jittered, about its original position, thesame pair(s) of capsules may be used for very rapid calculations. Thedepth may be defined as how close the tooth is to another tooth, e.g.,in mm of overlap. In some variation, the method and/or apparatus mayalternatively measure the space between the two closest capsules (e.g.,even when not colliding).

In use, the method of solving for the magnitude and velocity of acollision may be integrated into a method for solving for one or moretreatment plans. For example, the treatment plan solver may call on thecollision detector to identify the collision and rotation between eachtooth. The treatment plan solver may have initially identified digitalmodels of the patient's teeth in which one or more surfaces were modeledby 3D figures such as capsules. See, e.g., FIGS. 38 and 39. Thepatient's teeth, e.g., along the interproximal regions, may be modeledas individual teeth (or set of teeth) and the overlap 3509 may bedetermined. The teeth do not need to be re-modeled when makingadditional collisions determinations. The collision detector (collisionengine) may measure the change in magnitude as a collision depth, andmay also determine the velocity of the changing magnitude for each of aplurality of axes.

A special variant of the method is used during construction oforthodontic treatment with a non-linear optimization based algorithm.For example, to compute gradients of change of collision or spaceamount, every step of a non-linear optimization algorithm may computevalues for thousands of small variations of teeth positions. The resultof previous computations may be used to select smaller number ofcapsules that must be considered to find the amount of collision orspace, provided the change of position was limited by a small constantbound. This additional pruning reduces computational complexity fromO(N²) to O(1), and allows an increase in the number of capsules used intooth approximation without corresponding increase of computation time,increasing the precision.

In examples in which the capsules have a planar figure (e.g., line,rectangle, etc.) in the core, and an outer surface extending a constantradius from the core in x, y and z, collisions (e.g., overlap) betweenthe teeth may be analytically determined from the 3D shapes with highprecision. These systems and methods may also be applied to justadjacent portion of the teeth (rather than the entire teeth) and may becombined with a hierarchy of bounding boxes in order to accelerate thecomputation, as described above.

Any of the methods and apparatuses described herein, includingsubcomponents or subsystems (e.g., such as system or subsystem forautomatically detecting collisions between teeth, which may be referredto as collision detectors) may be configured for constructingapproximated shapes of teeth by packing the surface(s) of the teeth, orin some variations, other structures (e.g., attachments, brackets, etc.)using multiple three dimensional (3D) shapes (such as capsules), asdescribed above, and these 3D shapes (“capsules”) may be selected basedon the shape(s) of the product being modeled, including teeth and/orother structures, such as retainers, attachments, etc. As describesabove, in general approximation of shapes using the capsules as allows adramatic reduction in the time necessary for collision computationswhich may be a bottleneck in treatment plans construction. However evenif the accuracy of approximation is not high, a filling (e.g.,capsule-based) technique may still be useful in eliminating remainingcollisions when modeling. In some variations, the construction ofhigh-precision approximations can result in significant time savingseven without requiring a refinement of treatment plans with precisecomputations.

For example, in some variations topographical information about theface(s) of the teeth or other targets being modeled may be used toselect the size, shape and/or position of the capsules. In somevariations topological information about faces (such as curvatures) isused to find regions best suitable for approximation with singlecapsule. This may be accomplished by identifying one or more areas on ashape having a closed curvature; in some variations, when the capsulesconsists of spheres of fixed radius, or shapes based on a fixed radius,they may not efficiently approximate areas that have differentcurvatures. FIG. 41A illustrates one example of a pair of tooth shapesshowing regions having close (closed) curvatures that may beapproximated using a single capsule. In FIG. 41A, each of the differentregions (shown by different shading), e.g., 4101, 4103, has a closecurvature. Use quadric error metric to measure distance from shape toapproximation. Any appropriate method may be used to determine thecurvature of the surface.

Once identified, the curvature may be used to determine the shape, sizeand/or position of the capsules. Capsule approximations may be refinedon the fly. For example information about approximation quality indifferent regions may be determined, stored, and used to refineapproximations interactively if collision was requested in a particular(e.g., a “bad” region, or region of high error, as shown in FIG. 41B).In FIG. 41B, the shaded dots of different sizes show regions havingapproximation errors (e.g., the relative sizes of the dots 4109, 4109′in FIG. 41B reflect the approximation error at each dot position).

For example, described herein are methods of determining/detectingcollisions as described above, in which an initial partitioning of thethree-dimensional shape(s) (e.g., teeth) may be based on curvatures ofthe outer shape surface. Thus, the method, or any apparatus configuredto perform it, may identify a face of the outer surface that is close.For each face, the method or apparatus may construct a vector withcoordinates (x1, . . . , x7) where x1 . . . x3 are coordinates of centerof a face, x4 . . . x6 are coordinates of vector(k₁*d₁+k₂*d₂){circumflex over ( )}n (k₁, k₂ are principal curvatures offace, d₁, d₂ are principal directions, and n is normal to face), and x7is a mean curvature of a face defined as k₁+k₂.

A clustering algorithm may then be used with the constructed set ofvectors, and the number of clusters should be equal to desired number ofcapsules. In this technique, the center of each cluster may be used toconstruct a capsule to be used by an optimization algorithm as aninitial guess. A quadric error metric may be used to controlapproximation sticking from 3D shape; for measuring a distance between acapsule and a plane, the following definition may be used:

Distance(Capsule,Plane)=min(quadric error metric(s(t,r),Plane))

In this technique, t belongs to [0,1], s(t) is sphere with centerp0+t*(p1−p0), p0 and p1 denote end points of capsule, r is radius ofcapsule. This metric differs from the distance from an un-oriented pointp (as opposed to a plane {p, n}) to a capsule; it also takes intoaccount the orientation of the normals, and distinguishes naturallybetween convex and concave regions.

As mentioned above, any of these methods may include refinement ofcapsules on the fly. For example, after an approximation is computed,the apparatus or method may include marking poorly approximated areaswith marker (e.g., flag). A collision computation may check if anypoorly approximated areas lie near a potential collision area; if so,the method or apparatus may perform a capsule construction for theaffected areas (near potential collisions; other regions with a lowprobability of collisions may be ignored, even if poorly approximated).Newly constructed capsules may then be added to the approximation, andthe collision results may be recalculated using the newly constructedcapsules.

The methods described above may be used to dramatically increase thespeed and/or efficiencies of these techniques. For example, FIG. 41Cillustrates an example of a comparison between collision detection usingcapsule approximations at different levels of precision. In FIG. 41C,the right side 4133 is an approximation of a tooth in which 70 capsulesare used to approximate the tooth surface (e.g., 70 capsules per tooth),while the right side 4135 is an approximation using 300 capsules pertooth. The approximation using 70 capsules per tooth was over 20× faster(e.g., taking 10-15 seconds for the reconstruction) than a precisecollision detection method (e.g., using a triangular mesh), while the300 capsules per tooth was between 3×-7× faster (e.g., taking >1 minutefor the reconstruction). The 70 capsules/tooth 4133 example may beconsidered a “moderate precision” technique, having a differencecompared to a precise model of approximately 0.1 mm, while the 300capsules/tooth 4135 example is a higher precision model, having adifference compared to a precise model of approximately 0.03 mm.

EXAMPLE

An example of a method for generating an optimal partial treatment planmay include, for example, determining (in a computer processor) aninitial position of each of the patient's teeth (position andorientation, in six variables) from a digital model of the patient'steeth. The digital model can be the upper jaw, lower jaw or both upperand lower jaws. The software typically divides the models intoindividual teeth and positions them into patients bite relationship. Thesteps of determining the position of the patient's teeth may be done inthe same processor (or as part of the same device) that does the rest ofthe method (e.g., solves for the solution vector) or it may be adifferent, separate processor. Any of these methods may then determininga comprehensive (e.g., “optimal”) final position of the patient's teeth.

A processor performing the method may then receive product definition(e.g., number of stages to be used) specific to the patient treatment.Other product information may include: maximum allowed number of stages,whether attachments are allowed, maximum allowed root movements, crownmovements and rotations, etc.

Thereafter the processor may receive preferences (e.g., interproximalreduction, attachments, tooth/teeth that don't move, etc.) specific tothe patient treatment. Preferences may include: indicating whichtooth/teeth are not to move, individual teeth where attachments shouldnot be placed, arch to treat (both jaws, only lower or only upper),class correction amount and method, IPR, arch expansion, spaces,levelling preferences, etc.

The processor may then express a plurality of treatment targets of thetreatment plan as numerical functions (“target functions”) based on theproduct definition and preferences, weight each numerical function, andsum them to form a single numerical function. This single numericalfunction may include a weighted sum of at least, for example: toothposition compared to the comprehensive final position of the patient'steeth, misalignment (x- and z-misalignment, alignment to arch), diastema(spaces between neighboring teeth), collisions (inter arch collisions),and length of treatment (number of stages). Thus, the single numericalfunction (e.g., the merit function) is a nonlinear combination oftreatment targets (target functions) weighted by pre-definedcoefficients. Typically, key components of the merit function areobjective (independent of the comprehensive position) measurements ofaesthetic concerns: misalignment between teeth, spacing between teeth,amount of overjet and amount of overbite. Components that are relativeto comprehensive final position mostly describe orthodontic goals (archform, occlusion, levelling, alignment, etc.).

The pre-defined coefficients may be set or determined empirically, e.g.,by expert opinion, or may be solved. For example, starting from initialguess where weights are roughly same, setups may be prepared for casesfrom an existing database and reviewed. In addition, some adjustmentscan be made for technical reasons (i.e. to improve converging to asolution, which may be delayed if weights are inconsistent).

Constraints on tooth movements may then be expressed as numeric limitsbased on the product definition, preferences and comprehensive finalposition, including at least: the maximum velocity of tooth movement,maximum amount of collision, tooth movement limitations, stagingconstrains, and maximum amount of occlusion. As discussed above, otherconstraints may include: the maximum velocity of tooth movement, maximumamount of collision and space, tooth movement limitations, stagingconstrains, maximum amount of occlusion, amount of overbite, overjet,and midline position.

The single numerical function subject to the constraints on the toothmovements may then be solved (e.g., minimized) using a constrainedoptimization algorithm to get a solution vector and map the vector to atreatment plan. One example of a constrained optimization algorithm isthe Interior Point method, including Interior Point method variationsSQP and Active Set. Other methods may alternatively or also be used.

The solution vector is produced as a result of solving the constrainedoptimization algorithm. The optimization problem is defined as findingthe values of variables x₁ . . . x_(N) that minimize merit functionf₀(x₁ . . . x_(N)) and do not violate inequality constraints f_(i)(x₁ .. . x_(N)). Solution vector is the values of x₁ . . . x_(N) thatoptimization algorithm produced as an output. Variables are mappedpositions teeth, for every key-frame on every tooth there are sevenvariables: x, y, z coordinates, angulation, inclination and rotationangles, and stage number of the key-frame. For example, x₁, x₂, x₃, x₄,x₅, x₆ may be the initial position of molar, x₇ would be constant stage0 (initial), then x₈ . . . x₁₄ would be position, angles and stagenumber of intermediate key-frame added to molar for staging, then x₁₅ .. . x₂i are final position of the molar and final stage number (lengthof treatment). Then x₂₂ . . . x₄₃ are initial, intermediate and finalpositions and stage numbers of pre-molar, and it continues for everytooth. There may be different number of intermediate, staging key-frameson each tooth, so 14 variables per tooth at minimum, to 42 and morevariables for teeth with many staging key-frames). If multipleintermediate key-frames are present on a single tooth and their order isnot fixed, each coordinate (such as angulation) of tooth at everykey-frame may be calculated instead as a sum of piecewise functionsparametrized by the stage number and coordinate variables. The piecewisefunctions may be defined so that if x_(i) . . . x_(i+6) variablescorresponding to six coordinates at a key-frame are equal to zero, toothmovement through this key-frame is linear, which is equivalent toabsence of key-frame.

FIGS. 26A-26B illustrate one example of a set of key frames. Key framesare described in greater detail in U.S. Pat. Nos. 8,038,444 and6,729,876, herein incorporated by reference in their entirety. Thenumber of key frames used may be predetermined, or may be determined bythe apparatus or method. Each tooth may have a different number of keyframes.

Key frames may be used to simplify the treatment plans. For example,treatment plants may be stored as positions of key frames of everytooth. A key frame is essentially an animation of teeth movement fromposition at initial stage, through all key-frame positions to theposition at a final stage. Thus, the treatment plan does not need tostore positions for every stage. Defined positions may be at initial,final, and one or more intermediate stages that are referred to as keyframes. The position of tooth on a stage that is not a key frame isinterpolated between the two adjacent key frames. Thus, as mentionedabove, staging, i.e., intermediate positions, of each tooth may be alinear combination of several functional component. Each componentdescribes deviation from linear movement at a certain stage and isparameterized by six coordinate deviations and a stage number.

User-Specific Treatment Preferences

The methods and apparatuses described herein typically use treatmentpreferences to, in part, define the target functions (and thereforemerit function) and constraints that are then used to automaticallypre-calculate one or more treatment plans. Each user (e.g., dentalprofessional) may use the same general treatment preferences whentreating different patients. It would be very helpful to customizetreatment plan generation (and display) to the users, particularly asthe same users may worth with many patients.

For example, it would be beneficial to personalize treatment planningautomation for all users (e.g., dental professionals). This may be doneusing domain-specific language that can be integrated into the methodsand apparatuses described herein. For example, the start of anytreatment (including patient consultation) may include a questionnaireor template that the user completes. The treatment planning optimizationengine may use a treatment template described with a domain specificlanguage in order to control case processing flow to create treatmentaccording to personal needs of the user.

There may be two sources of dental professional's preferences on how toprepare treatment plans. One source of treatment preferences which maybe essentially a structured input where for a set of questions, the userprovides answers, where each answer is a selection from a set ofpredefined answers. The second source of information may be representedas a text-based comments which defines the user's personal rules tofollow when preparing a treatment plan for a doctor. Domain specificlanguage may be used to store user's non-structure input (e.g., textcomments describing his treatment preferences) which may enable fullautomation of treatment planning as well as aggregation of rules frommultiple sources (for example, structured preferences and non-structuredtreatment preferences).

Structured treatment preferences may cover only a small portion ofusers' personal treatment protocols. Instead, much of the treatmentprotocol details may be provided by the user in non-structured, textform. While setting up a treatment plan, a technicians uses bothstructured treatment preferences and non-structured treatmentpreferences. If this information were used manually, when a technicianapplies text-based user preferences, misinterpretation and inconsistencyin treatment plan quality may result, and the resulting treatment planmay depend on the technician. As described herein, text-based commentsexpressing doctors treatment planning style may be converted into adomain-specific language (manually or automatically) and the methods orapparatus (e.g., software) may interpret this domain-specific languageto automatically apply doctors preferences for treatment planningpreparation.

From the users perspective, the user fills two sections of hispreferences describing his treatment style, e.g., on a web site. Onesection may be represented as questions with predefined set of answerseach, and another second may be text-form comments. The user may thensaves her preferences, and both types of preferences may then be appliedto cases associated with (e.g., submitted by) this user.

The user's text-based preferences may be transformed into adomain-specific language which defines clinical rules to apply fortreatment planning in a formal way which also may be interpreted byTreat treatment planning software. This may initially be performedmanually or semi-automatically, and may initially include manual reviewand checking (including checking with the user). However, once thedomain-specific language is constructed for that user, it may be usedwithout requiring manual intervention, unless modified at the user'srequest (e.g., when displaying the resulting treatment plans, asdescribed herein). Each user may be associated with a rules file thatmay be unique to the user and may be updated independently from otherusers.

When case is submitted by a user (e.g., requesting a treatment plan),the user's preferences, expressed in a form of a domain-specificlanguage, may be accessed from the stored database and aggregated withother user preferences (e.g. patient-specific target preferences oradditional structured input provided by the user) and may be used toexecute the fully automated treatment planning described above.

FIG. 27 illustrates one method of defining user-specific treatmentpreferences based on both structured and unstructured input. Forexample, in FIG. 27, the method (or any apparatus configured to performthis method, which may be a treatment plan optimizing engine ortreatment plan optimizing generator) may first acquire a set of texturalinstructions (e.g., unscripted instructions) from a user (e.g. a dentalprofessional such as a dentist, orthodontist, etc.) 2701. These may betyped or handwritten (and converted to a machine readable form) and thenconverted into a domain-specific language specific to the user; thisrepresents a first set of rules (treatment preferences). As mentionedabove, this step may be initially performed semi-automatically ormanually to build the domain-specific language. Once built, it may befully automatic 2705.

Concurrently or sequentially, the method may acquire a set of scriptedinstructions from the user. The scripted instructions may compriseresponses from a script of predefined choices (e.g., a survey,questionnaire, etc.) 2703. The responses to the set of scriptedinstructions may be automatically converted into a second set of rules(treatment preferences) 2707. Thereafter, the method may includeaccessing, by the automated treatment planning engine, the first set oftreatment preferences and the second set of treatment preferences, andforming a combined set of treatment preferences from them 2709. Theautomated treatment planning engine may then access (e.g., receive,look-up, etc.), a digital model of the patient's teeth 2711, and any ofthe other inputs necessary to automatically generate a treatment planfor the patient's teeth using the combined set of treatment preferencesthe digital model of the patient's teeth, a comprehensive model of thepatient's teeth and/or treatment details (e.g., product details), asalready described above 2713.

FIG. 28 illustrates another example of this. In this example, thetreatment plan optimizing engine or treatment plan optimizing generator2813 includes a rules aggregator 2815 that combines the treatmentpreferences from user-specific treatment preferences that are stored ina database indexed by user 2805 that are converted via a domain-specificlanguage 2803 into a first set of treatment rules, along with the user'spatient-specific treatment preferences (specific to the instant case)2811 that may also be converted by the domain-specific language 2819into rules, and these rules may be combined 2815, then converted intotreatment preferences using a language interpretation module 2817. Theinterpretation of these rules into treatment preferences may depend inpart on the product (e.g., aligner features 2821), and may be providedto for determining staging 2823 and the optimal (e.g., comprehensive)final position 2825.

Thus, a set of rules may be expressed in a domain specific languages andassociated with each user in a clinical database. A module may convertsstructured input (e.g., answers given by a doctor on a set of questions)into additional set of rules. These rules may be combined via a rulesaggregation module which combines rules from multiple sources into asingle rules list. The language interpretation module may takes any ofthese rules files as an input and interpret it to control the flow ofFiPos, Staging and Aligner Features modules in order to create atreatment plan fully automatically, as described above.

Automatic Selection Treatment Plans

The methods and apparatuses described herein may provide multipletreatment plans and may allow the user (e.g., the dentist, orthodontist,dental professions) and/or in some variations the patient, to view allor a subset of these treatment plans, and to select one or more of theseplans from which a series of dental appliances to be manufacturedtreatment. As described above, a very large number (e.g., 12, 18, 24,30, 36, 40, 48, 50, 55, 60, 65, 70, 75, 100, 125, etc.) of treatmentplans may be generated concurrently. Ordering or organizing thetreatment plans, and in particular, determining the order of whichtreatment plans to display and/or how the user may toggle or selectbetween these different treatment plans may therefore be helpful.

In any of these variations, the treatment plans may be sorted ororganized by assigning a weight to each treatment plan based one or morecriterion. For example, if 24 different treatment plans are generated,it would be helpful to automatically order the treatment plans using oneor more criterion and to display them in that order. For example, thetreatment plans may be ordered (assigned weights) and displayed basedhow comprehensive they are. The degree of comprehensiveness may be basedon, for example, how closely the predicted final position of the toothresembles the ideal final position of the patient's teeth (or anarbitrary final position) that is calculated as part of the procedurefor generating the multiple treatment plans described above.

In some variations, different categories of treatment plans may bedisplayed concurrently, e.g., the most comprehensive treatment plansamong treatment plans having a first characteristic (such as a thosetreatment plans limited to a first number of stages, e.g., 16 stages)may be displayed alongside the most comprehensive treatment plans havinga second characteristic (such as those treatment plans limited to asecond number of stages, e.g., 24 stages, or unlimited stages). Themethods and systems described herein may determine how comprehensiveeach treatment plan is by comparing to the ideal final position and/orby applying ranking logic in which the each of one or morecharacteristics (also referred to herein as criterion) are used todetermine the weighting. For example, treatment plans with interproximalreduction (IPR) may be weighted more than plans without IPR; treatmentsplans with extraction may be weighted higher; treatment plans with allattachments (e.g., anterior and posterior) may be weighted higher thanplans without attachments, plans with only anterior attachments may beranked higher than those with only posterior attachments, treatmentplans including both upper and lower arch may be ranked higher thankthose with only one of the dental arches; upper arch only treatmentplans may be ranked higher than lower arch only, etc. Each of thesecharacteristics may provide a number of points (weights) and the finalranking may be determined by the sum of these points for each treatmentplan.

In addition to, or instead of, ordering the plurality of treatment plansbased on the comprehensiveness of each treatment plan, the methods andapparatuses described herein may order the treatment plans based on oneor more alternative or additional criterion, such as: the duration ofthe treatment plan, the number of stages, the amount of tooth movementachieved, etc. The criterion may be user selected or automaticallyselected. In some variations, the criterion may include, for example, aprediction of a user preference; the user's preference may be determinedby machine learning, and may be specific to the user (e.g., based onprior/past preferences or selections for that user) or it may begeneric.

For example, in any of these variations, the system may select two ofthe sorted treatment plans for side-by-side (concurrent) display; insome variations along with the original tooth position and/or the idealtooth position calculated. As mentioned, the system may select thehighest-ranked treatment plans within two (or more) categories forconcurrent display. The ranked treatment plans may be displayed in aninitial user interface screen, from which the user may then togglebetween other treatment plans using one or more controls on the userinterface, as described herein. In some variations, the system selectstwo of the most comprehensive treatment plans and show them to the userin an initial display for user review (e.g., using a treatment reviewsystem or sub-system). The system may weight each treatment plan basedon the one or more criterion. For example, the system may weights ofeach treatment plan based on attributes such as IPR, use of attachments(and type of attachments, and/or number of attachments, and/or whereattachments are used), presence or single arch or dual arch treatmentfor treatment plan, etc. As mentioned above, these criterion may also beused to select categories for concurrent display. The apparatus may sortand return the most comprehensive for the case.

FIG. 42 illustrates one example of a display showing side-by-side(concurrent) display of the sorted treatment plans (sorted forcomprehensiveness based, e.g., clinical efficiency using rankedcriterion). In this example, the first display screen shows the finaltooth positon for plans with highest ranking in each of two categories:a first product, “Invisalign GO Plus” and a second category “InvisalignGo” product). A user can start review them without spending time tobrowse plans and finding best ones. Thus, the system and method maydefault to showing the highest-ranked treatment plans first, wheretreatment plans are ranked as described herein. In FIG. 42, the leftside image 4201 shows the initial position of the patient's teeth. Theright-side images may be images of the final tooth position for thehighest-ranked treatment programs in two categories. For example, themiddle image 4203 may the highest-ranked treatment program among thosequalifying as the first product (“Invisalign GO Plus”, e.g. limited to12 or fewer stages). The right-side image 4205 may be the highest-rankedtreatment program among those qualifying as the second product (e.g.,“Invisalign GO” product, limited to 20 or fewer stages). This displayview may be referred to as a multiple cards view. The display may alsoindicate features used as part of the calculations done on eachtreatment plan, such as the use/type of attachments 4211, theuse/non-use of IPR 4201, the movement of both arches 4213, the productused 4215, etc. The display may also indicate the number of stages inthe treatment plan 4217. As will be described below, in some variationsthese indicators may be selectable controls, e.g., drop-down menus,buttons, etc., that may allow the user to toggle between treatmentplans.

In practice, when generating the one or more treatment plans, the systemmay set up how to rank the treatment plans for initial display, e.g., inthe multiple cards display. For example, the system may look at all or asubset of the parameters used when calculating the multiple differenttreatment plans, including but not limited to: information about IPR(e.g., IPR used/IPR not used); information about attachments set (e.g.,attachments: Yes/attachments: Posteriors only/attachments: No); archesto treat (single arch treatment/dual arch treatment); treatment type(“Invisalign Go”/“Invisalign Go Plus”), etc.

In some variations, if only one Product Type is available for theDoctor, then only one Treatment Plan shall be shown in the MultipleCards View by default. Alternatively, in some variations, the multiplecards display may be used to display single arch/both arch views orother parameters. For single arch treatments submitted by the user, themost comprehensive single arch treatment plan may be selected and shownin the Multiple Cards View for each available product type.

As mentioned above, the each of the generated treatment plans may beranked (e.g., scored). For example, table 1 (FIG. 43A) illustrates oneexample of a ranking of priorities that may be used to pick the mostcomprehensive single arch treatment plan within one treatment type to beshown to the user. In this example, lower numbers are higher ranked(e.g., 1 is the highest priority, 11 is the lowest priority). Thesimplified table of FIG. 43A shows the relationship between twocategories (IPR and attachments) that may have two or more differentstates; other categories may be included, adding multiple dimensions.FIG. 43B is a table illustrating another example of a set of rankingsfor dual arch treatment; the same categories apply. Thus, whendetermining a ranking score for each treatment plan, the system may usea look-up table (or tables) similar to the tables shown in FIGS.43A-43B, or it may apply a scoring system in which a particular numberof “points” may be assigned for each parameter state (though note thatthis may result in ‘ties’ that may be permitted or reconciled usingsecond set of preferences).

In the example of scoring using FIGS. 43A and 43B, when determining theinitial display, the treatment plan with the lowest value score may bedisplayed. In variations in which one or more option are not availableto the user (e.g., only one Product Type is available for the doctor,the user is not able/willing to provide IPR, etc.) then treatment plans,if generated, may be scored lower or removed. In some instances, even ifnot selected by the user (if, for example, the user indicates “no IPR”),treatment plans including these options may still be generated, so thatthe user can compare the use/non-use of these options directly.

From the initial view, the user may select one or more of the treatmentplans for side-by-side comparison with other selected treatment plansand may begin to look though other (lower ranked) treatment plans bycontrolling the options/criterion. For example, the screen may include a“compare” or “save” control (e.g., button) that may allow the user tostore this case for analysis. In some variations, a control may be usedto move a selected treatment plan to one side of the display (e.g., insome variations replacing the initial view of the patient's teeth) sothat it can be directly compared to other treatment plans.

In addition to directly toggling between options on the user interface,a control may also be provided to allow the user to see the next-rankedtreatment plan (e.g., a button, or other control on the user interface,etc.). For example, selecting a “compare” button in the Multiple Cardsview may be used for showing, in a dual arch treatment case, the nexttreatment plan according to the priorities scaling/ranking describedabove, such as in Table 2 of FIG. 43B. Clicking the same control (e.g.,a “compare” button in the Multiple Cards view) for the single archtreatment case, will pick the next treatment plan according prioritiesdescribed in both Tables 1 and 2 (e.g., FIGS. 43A and 43B). In oneexample, both treatment types are available for the user (e.g.,Invisalign Go and Invisalign Go Plus), then clicking on “Compare” buttonin the Multiple Cards view, the system may pick the most comprehensivetreatment plan with the Product Type which is absent in that view usingFIG. 43A for the single arch treatments and using, e.g., Table 2 for theDual Arch treatments. In some variations, the “Invisalign Go Plus”program may generate a treatment plan that can be shown in the MultipleCards view (e.g., on the left) by default if both treatment types areshown. In some variations the Invisalign Go Treatment Plan may be shownat the right in the Multiple Cards view by default (e.g., if bothtreatment types are present).

Treatment Plan Filters

As discussed above, any of the methods and apparatuses described hereinmay be configured to display one or more treatment plans, typically byshowing one or more of the model of the patient's dental arch(es) at oneor more stages in the treatment plan, and allowing the user to toggle orswitch between treatment plans by changing which parameters orconstraints specified when generating the treatment plans. Thus, a usermay select, in real-time, an appropriate treatment plan by usingfilters, toggles, or switches against the clinical parameters, such asone or more of: interproximal reduction (No IPR/No, IPR), Attachments(all attachments, No Attachments, anterior only attachments, posterioronly attachments, etc.), etc. These controls may be referred to asclinical filters and the user may select the most appropriate treatmentplan for the particular patient using these clinical filters to rapidlycompare treatment plans. Using clinical filters may also allow the userto fine-tune a selected treatment plan. For example, in some variationsthe user may select another value for IPR or attachments using thefilters and may then immediately submit the modified treatment plan togenerate a new family of modified treatment plans that may be viewedimmediately or shortly thereafter.

Thus, by toggling between treatment plans, the user may automaticallyand quickly browse between multiple treatment plans by choosing keyfeatures that can affects final position, such as the use and placementof attachments, IPRs, treatment of one or both arches, etc. Each filtercan display one or more notification or tip if the feature is notavailable for a particular case.

For example, FIG. 44 is a mock-up of a multi-card view that shows threepanels. The first panel shows an image (3D model from a scan) of thepatient's current teeth 4401. The middle panel shows an image of thepatient's teeth from a first treatment plan 4403 (e.g., a treatment planhaving 9 stages, using the constraints of the “Invisalign Go Plus”product, which has a limited number of stages permitted, in which IPRwas not used, no attachments were used, and aligners are used on botharches). Similarly, the third panel shows an image of the patient'steeth from a second treatment plan 4405 (e.g., a treatment plan having11 stages, using the constrains of the “Invisalign Go Plus” product, inwhich IPR was not used, but posterior only attachments is being selectedby a user using the control or filter, shown here as a button on theuser interface that pulls out a drop-down menu allowing the user tospecify which type of attachments are use (e.g., no attachments, yesattachments or posterior only attachments); in FIG. 44, the user ispreparing to select “attachments posterior only” to switch the thirdcard to display this variation

In general the displays showing the initial malocclusion 4401 and thedifferent treatment plans 4403 and 4405 may show a flat or static viewof the teeth based on the simulated movement per the treatment plan;alternatively an animation may be used, showing tooth movement acrossmultiple stages of treatment. In some variations, the stage shown may bethe final stage (showing all movement); other stages may also be shown.In some variations the 3D model showing the tooth position may berotated (or may rotate automatically) to show different perspectives.

As mentioned above, a filter may indicate one or more notification ortip if the feature is not available for a particular case. For example,FIG. 45 illustrates a display similar to that shown in FIG. 44, showingside-by-side comparisons of the original tooth positions, and twotreatment plans. In this example, although the display includes anindicator/control the number of arches (e.g., both arches, single arch)only treatment plans with a single arch were generated, and therefore ifthe user attempts to switch to view ‘single arch’ treatment plans, asshown in the middle image, a notification 4505 indicating that only dualtreatment is available may be provided. In some variations the indicatormay be grayed out, preventing it from being selected.

In general, any of these displays may also include an indication of thecost or price associated with the treatment plan. For example, one ofthe filters may allow the doctor to compare two different product typeshaving different price. Higher price products may have, for example,more stages in the treatment and have a wider range for clinicalconditions. Thus, in any of these examples, the doctor may use filtersto provide an overview of what treatments (e.g., what treatmentoutcomes) may be best for the patient and which may be automaticallysuggested by the system, as described above, for a particular patient.In some variations, the doctor can use these filters to review aparticular clinical feature usage (e.g., comparing one plan with IPR toanother plan without IPR, etc.) and compare results. The use of filtersmay also allow a user to see clinical details for the selected plan.

Filters may also be applied when reviewing a single plan in greaterdetail, as illustrated in FIG. 46. This view may be referred to as a“single treatment plan” view (STP view). In contrast, the views shown inFIGS. 44 and 45 may be referred to as “multiple treatment plan views”(MTP views). In the example shown in FIG. 46, the same controls (e.g.,configured as filters) may be included; in addition, the user may selectwhich stage 4603 to review or to animate between them. In addition, theuser interface may include one or more controls for modifying thetreatment plan 4613. For example, the user may select ‘modify” and mayuse a tool to add/remove attachments 4607 and/or pontics, move theattachment, indicate IPR 4605, etc. Finally, if the treatment plan looksgood, the user may indicate approval 4615.

In general, the user may also switch between multiple treatment planviews and single treatment plan views. For example, FIG. 47 showsanother example of a multiple treatment plan view similar to thatdescribed above, showing a side-by-side comparison between two (or more)treatment plans, as well as the patient's original tooth configuration(“initial malocclusion”). The MTP view may show essential high-levelinformation about the projected outcomes of the multiple alternativetreatments and initial malocclusion. In contrast, the STP view may showhow to achieve the selected treatment plan. Switching between thesedifferent views may help the user review the selected plan(s) andmaximized to whole screen. In FIG. 47, the user may select one of thetreatment plans displayed by actuating the control (shown as a button4705, 4705′ labeled “view” on the user interface). To open a SingleTreatment Plan view (also referred to herein as a Single Card View) froma Multiple Cards (multiple treatment plan view), the user may selectthis control as shown in FIG. 47. This may open up the single treatmentplan view of that treatment plan, as shown in FIG. 48. The STP mayinclude features not in the MPT display, such as, for example: playstaging, free form commenting, editing/modification of the treatmentplan, etc. The user may also switch back to the multiple view by, forexample, selecting a control 4805 for MTP, or “back”.

The single treatment plan display (e.g., user interface) may allow theuser to review staging, features available on each stage of thetreatment, and teeth position on each stage. As shown in FIG. 49, insome variations the STP view may allow a user to approve the selectedplan and send it to manufacturing or to add free form comments 4905,asking the manufacturing technician to modify (e.g., improve or change)anything in this treatment plan and send the treatment plan(s) back tothe technician for a treatment plan update 4907, which may be manually,automatically or semi-automatically performed. In some variations, theuser may view details for any plan in a MTP view by clicking on a “view”control (e.g., button). In some variations, the STP view may allow thedoctor to see detailed staging info at the bottom of the screen, suchas: treatment length for upper and lower arches, what type of alignerswill be manufactured for each stage (active or passive), overcorrectionstages if they are present for the treatment, animated controls toplay/pause treatment animation, etc.

In any of these views, tools (e.g., on the toolbar) may be used to allowthe user to review and/or modify features on any stage (attachments,IPRs, pontics, etc.), as discussed above in reference to FIG. 46. Forexample, the user may click on an “approve” control (e.g., button) tosend the selected treatment plan directly to manufacturing.Alternatively, clicking on a “modify” control (e.g., button) mayadd/edit free form comments and send the case to a technician for anupdate after actuating a “submit” control 4907.

Any of the methods (including user interfaces) described herein may beimplemented as software, hardware or firmware, and may be described as anon-transitory computer-readable storage medium storing a set ofinstructions capable of being executed by a processor (e.g., computer,tablet, smartphone, etc.), that when executed by the processor causesthe processor to control perform any of the steps, including but notlimited to: displaying, communicating with the user, analyzing,modifying parameters (including timing, frequency, intensity, etc.),determining, alerting, or the like.

When a feature or element is herein referred to as being “on” anotherfeature or element, it can be directly on the other feature or elementor intervening features and/or elements may also be present. Incontrast, when a feature or element is referred to as being “directlyon” another feature or element, there are no intervening features orelements present. It will also be understood that, when a feature orelement is referred to as being “connected”, “attached” or “coupled” toanother feature or element, it can be directly connected, attached orcoupled to the other feature or element or intervening features orelements may be present. In contrast, when a feature or element isreferred to as being “directly connected”, “directly attached” or“directly coupled” to another feature or element, there are nointervening features or elements present. Although described or shownwith respect to one embodiment, the features and elements so describedor shown can apply to other embodiments. It will also be appreciated bythose of skill in the art that references to a structure or feature thatis disposed “adjacent” another feature may have portions that overlap orunderlie the adjacent feature.

Terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention.For example, as used herein, the singular forms “a”, “an” and “the” areintended to include the plural forms as well, unless the context clearlyindicates otherwise. It will be further understood that the terms“comprises” and/or “comprising,” when used in this specification,specify the presence of stated features, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, steps, operations, elements, components, and/orgroups thereof. As used herein, the term “and/or” includes any and allcombinations of one or more of the associated listed items and may beabbreviated as “/”.

Spatially relative terms, such as “under”, “below”, “lower”, “over”,“upper” and the like, may be used herein for ease of description todescribe one element or feature's relationship to another element(s) orfeature(s) as illustrated in the figures. It will be understood that thespatially relative terms are intended to encompass differentorientations of the device in use or operation in addition to theorientation depicted in the figures. For example, if a device in thefigures is inverted, elements described as “under” or “beneath” otherelements or features would then be oriented “over” the other elements orfeatures. Thus, the exemplary term “under” can encompass both anorientation of over and under. The device may be otherwise oriented(rotated 90 degrees or at other orientations) and the spatially relativedescriptors used herein interpreted accordingly. Similarly, the terms“upwardly”, “downwardly”, “vertical”, “horizontal” and the like are usedherein for the purpose of explanation only unless specifically indicatedotherwise.

Although the terms “first” and “second” may be used herein to describevarious features/elements (including steps), these features/elementsshould not be limited by these terms, unless the context indicatesotherwise. These terms may be used to distinguish one feature/elementfrom another feature/element. Thus, a first feature/element discussedbelow could be termed a second feature/element, and similarly, a secondfeature/element discussed below could be termed a first feature/elementwithout departing from the teachings of the present invention.

Throughout this specification and the claims which follow, unless thecontext requires otherwise, the word “comprise”, and variations such as“comprises” and “comprising” means various components can be co-jointlyemployed in the methods and articles (e.g., compositions and apparatusesincluding device and methods). For example, the term “comprising” willbe understood to imply the inclusion of any stated elements or steps butnot the exclusion of any other elements or steps.

In general, any of the apparatuses and methods described herein shouldbe understood to be inclusive, but all or a sub-set of the componentsand/or steps may alternatively be exclusive, and may be expressed as“consisting of” or alternatively “consisting essentially of” the variouscomponents, steps, sub-components or sub-steps.

As used herein in the specification and claims, including as used in theexamples and unless otherwise expressly specified, all numbers may beread as if prefaced by the word “about” or “approximately,” even if theterm does not expressly appear. The phrase “about” or “approximately”may be used when describing magnitude and/or position to indicate thatthe value and/or position described is within a reasonable expectedrange of values and/or positions. For example, a numeric value may havea value that is +/−0.1% of the stated value (or range of values), +/−1%of the stated value (or range of values), +/−2% of the stated value (orrange of values), +/−5% of the stated value (or range of values), +/−10%of the stated value (or range of values), etc. Any numerical valuesgiven herein should also be understood to include about or approximatelythat value, unless the context indicates otherwise. For example, if thevalue “10” is disclosed, then “about 10” is also disclosed. Anynumerical range recited herein is intended to include all sub-rangessubsumed therein. It is also understood that when a value is disclosedthat “less than or equal to” the value, “greater than or equal to thevalue” and possible ranges between values are also disclosed, asappropriately understood by the skilled artisan. For example, if thevalue “X” is disclosed the “less than or equal to X” as well as “greaterthan or equal to X” (e.g., where X is a numerical value) is alsodisclosed. It is also understood that the throughout the application,data is provided in a number of different formats, and that this data,represents endpoints and starting points, and ranges for any combinationof the data points. For example, if a particular data point “10” and aparticular data point “15” are disclosed, it is understood that greaterthan, greater than or equal to, less than, less than or equal to, andequal to 10 and 15 are considered disclosed as well as between 10 and15. It is also understood that each unit between two particular unitsare also disclosed. For example, if 10 and 15 are disclosed, then 11,12, 13, and 14 are also disclosed.

Although various illustrative embodiments are described above, any of anumber of changes may be made to various embodiments without departingfrom the scope of the invention as described by the claims. For example,the order in which various described method steps are performed mayoften be changed in alternative embodiments, and in other alternativeembodiments one or more method steps may be skipped altogether. Optionalfeatures of various device and system embodiments may be included insome embodiments and not in others. Therefore, the foregoing descriptionis provided primarily for exemplary purposes and should not beinterpreted to limit the scope of the invention as it is set forth inthe claims.

The examples and illustrations included herein show, by way ofillustration and not of limitation, specific embodiments in which thesubject matter may be practiced. As mentioned, other embodiments may beutilized and derived there from, such that structural and logicalsubstitutions and changes may be made without departing from the scopeof this disclosure. Such embodiments of the inventive subject matter maybe referred to herein individually or collectively by the term“invention” merely for convenience and without intending to voluntarilylimit the scope of this application to any single invention or inventiveconcept, if more than one is, in fact, disclosed. Thus, althoughspecific embodiments have been illustrated and described herein, anyarrangement calculated to achieve the same purpose may be substitutedfor the specific embodiments shown. This disclosure is intended to coverany and all adaptations or variations of various embodiments.Combinations of the above embodiments, and other embodiments notspecifically described herein, will be apparent to those of skill in theart upon reviewing the above description.

What is claimed is:
 1. A method of creating a treatment plan to align apatient's teeth using a plurality of removable aligners to be worn insequential stages, the method comprising: receiving, in a processor, adigital model of a patient's teeth; accessing, by the processor, a setof treatment preferences, a comprehensive final position of thepatient's teeth, and a set of treatment details; selecting a pluralityof numerically expressed treatment targets from a memory accessible tothe processor, based on the set of treatment details, the set oftreatment preferences and the comprehensive final position of thepatient's teeth; combining the plurality of numerically expressedtreatment targets to form a single numerical function; selecting aplurality of numeric limits on the single numerical function based onthe set of treatment preferences; minimizing the single numericalfunction subject to the plurality of numeric limits to get a solutionvector including all stages forming the treatment plan; mapping thesolution vector to a treatment plan, wherein the treatment plan includesa final tooth position that is different from the comprehensive finalposition of the patient's teeth; and outputting the treatment plan. 2.The method of claim 1, further comprising receiving, in the processor:the digital model of a patient's teeth, the set of treatment preferencesor a reference to a set of treatment preferences, the comprehensivefinal position of the patient's teeth, and the set of treatment detailsor an identifier identifying the set of treatment details.
 3. The methodof claim 1, wherein the set of treatment preferences comprise one ormore of: an indicator of which teeth are not permitted to move, anindication of which teeth should not have an attachment, an indicator ofwhich teeth to treat, an indicator of tooth class correction amount, anindicator that interproximal reduction is to be used, an indicator thatarch expansion is to be used, and indicator of spacing between teeth, anindicator or tooth levelling.
 4. The method of claim 2, wherein theidentifier identifying the set of treatment details identifies a producthaving a defined set of treatment details accessible to the processor.5. The method of claim 1, wherein the set of treatment details comprisesone or more of: a maximum allowed number of stages, whether attachmentsto the patient's teeth are allowed, a maximum allowed tooth rootmovement, a maximum allowed tooth crown movement, and a maximum allowedtooth rotation.
 6. The method of claim 1, wherein combining thenumerically expressed treatment targets further comprises weighting eachof the numerically expressed treatment targets in the single numericalfunction.
 7. The method of claim 1, wherein the single numericalfunction includes, for a set of teeth, a sum of at least: a differencefrom an initial position of the patient's teeth compared to thecomprehensive final position of the patient's teeth, a measure ofmisalignment in an x direction for the patient's teeth, a measure ofmisalignment in a z direction for the patient's teeth, a measure ofmisalignment of a dental arch of the patient's teeth, a measure ofdiastema between neighboring teeth, a measure of overjet of the teeth, ameasure of overbite of the teeth, a measure of collisions between theteeth, a measure of the difference between an arch of the teeth and thecomprehensive final position of the patient's teeth, a measure of thedifference in leveling between the teeth and the comprehensive finalposition of the patient's teeth, a measure of an amount of occlusionbetween the teeth of the patient's upper and lower jaws, a measure ofthe difference in the amount of occlusion between the teeth and thecomprehensive final position of the patient's teeth, a measure of anamount of mesial to distal round trips of the teeth, a measure of theamount of buccal to lingual round trips of the teeth, and a measure of anumber of aligner stages compared to a target number of aligner stagesfrom the set of treatment details.
 8. The method of claim 1, wherein thesingle numerical function includes, for a set of teeth, a sum of atleast: a difference from an initial position of the patient's teethcompared to the comprehensive final position of the patient's teeth, ameasure of misalignment for the patient's teeth, and a measure of anumber of aligner stages compared to a target number of aligner stagesfrom the set of treatment details.
 9. The method of claim 1, furthercomprising adjusting the plurality of numerically expressed treatmenttargets into a plurality of adjusted numerically expressed treatmenttargets based on: the set of treatment details, the set of treatmentpreferences and the comprehensive final position of the patient's teeth,further wherein combining the plurality of numerically expressedtreatment targets comprises combining the plurality of adjustednumerically expressed treatment targets.
 10. The method of claim 1,wherein the plurality of numeric limits comprises one or more of: amaximum velocity of tooth movement, a maximum amount of collisionbetween teeth, a tooth movement limitation, a maximum number of alignerstages, a maximum amount of occlusion, a maximum amount of occlusion, amaximum amount of overbite, a maximum amount of overjet, and a maximummidline position.
 11. The method of claim 1, wherein minimizing thesingle numerical function subject to the plurality of numeric limitscomprises using a constrained optimization method to get a solutionvector.
 12. The method of claim 11, wherein the constrained optimizationmethod comprises an interior point method.
 13. The method of claim 1,wherein mapping the solution vector to a treatment plan comprisesconverting the solution vector into a set of key frames for each tooth,corresponding to a stage number, and positional information for eachtooth, including an x coordinate, a y coordinate, a z coordinate, and anangulation, an inclination and a rotation angle.
 14. The method of claim1, further comprising displaying the final tooth position of thetreatment plan.
 15. A method of creating a treatment plan to align apatient's teeth using a plurality of removable aligners to be worn insequential stages, the method comprising: receiving, in a processor, adigital model of a patient's teeth; accessing, by the processor, a setof treatment preferences, a comprehensive final position of thepatient's teeth, and a set of treatment details; selecting a pluralityof numerically expressed treatment targets from a memory accessible tothe processor based on: the set of treatment details, the set oftreatment preferences and the comprehensive final position of thepatient's teeth; adjusting the plurality of numerically expressedtreatment targets into a plurality of adjusted numerically expressedtreatment targets based on: the set of treatment details, the set oftreatment preferences and the comprehensive final position of thepatient's teeth; combining the plurality of adjusted numericallyexpressed treatment targets to form a single numerical function; settinga plurality of numeric limits on the single numerical function based onthe set of treatment preferences; iteratively minimizing the singlenumerical function subject to the plurality of numeric limits to get asolution vector including all stages forming the treatment plan; mappingthe solution vector to a treatment plan, wherein the treatment planincludes a final tooth position that is different from the comprehensivefinal position of the patient's teeth; and outputting the treatmentplan.
 16. A non-transient, computer-readable medium containing programinstructions for creating a treatment plan to align a patient's teethusing a plurality of removable aligners, the program instructionscausing a processor to: receive, in the processor, a digital model of apatient's teeth; access a set of treatment preferences, a comprehensivefinal position of the patient's teeth, and a set of treatment details;select a plurality of numerically expressed treatment targets from amemory accessible to the processor, based on the set of treatmentdetails, the set of treatment preferences and the comprehensive finalposition of the patient's teeth; combine the plurality of numericallyexpressed treatment targets to form a single numerical function; selecta plurality of numeric limits on the single numerical function based onthe set of treatment preferences; minimize the single numerical functionsubject to the plurality of numeric limits to get a solution vectorincluding all stages forming the treatment plan; and map the solutionvector to a treatment plan, wherein the treatment plan includes a finaltooth position that is different from the comprehensive final positionof the patient's teeth.
 17. The non-transient, computer-readable mediumof claim 16, wherein the set of treatment preferences comprise one ormore of: an indicator of which teeth are not permitted to move, anindication of which teeth should not have an attachment, an indicator ofwhich teeth to treat, an indicator of tooth class correction amount, anindicator that interproximal reduction is to be used, an indicator thatarch expansion is to be used, and indicator of spacing between teeth, anindicator or tooth levelling.
 18. The non-transient, computer-readablemedium of claim 16, wherein the set of treatment details comprises oneor more of: a maximum allowed number of stages, whether attachments tothe patient's teeth are allowed, a maximum allowed tooth root movement,a maximum allowed tooth crown movement, and a maximum allowed toothrotation.
 19. The non-transient, computer-readable medium of claim 16,wherein combining the numerically expressed treatment targets furthercomprises weighting each of the numerically expressed treatment targetsin the single numerical function.
 20. The non-transient,computer-readable medium of claim 16, wherein the single numericalfunction includes, for a set of teeth, a sum of at least: a differencefrom an initial position of the patient's teeth compared to thecomprehensive final position of the patient's teeth, a measure ofmisalignment in an x direction for the patient's teeth, a measure ofmisalignment in a z direction for the patient's teeth, a measure ofmisalignment of a dental arch of the patient's teeth, a measure ofdiastema between neighboring teeth, a measure of overjet of the teeth, ameasure of overbite of the teeth, a measure of collisions between theteeth, a measure of the difference between an arch of the teeth and thecomprehensive final position of the patient's teeth, a measure of thedifference in leveling between the teeth and the comprehensive finalposition of the patient's teeth, a measure of an amount of occlusionbetween the teeth of the patient's upper and lower jaws, a measure ofthe difference in the amount of occlusion between the teeth and thecomprehensive final position of the patient's teeth, a measure of anamount of mesial to distal round trips of the teeth, a measure of theamount of buccal to lingual round trips of the teeth, and a measure of anumber of aligner stages compared to a target number of aligner stagesfrom the set of treatment details.
 21. The non-transient,computer-readable medium of claim 16, wherein the single numericalfunction includes, for a set of teeth, a sum of at least: a differencefrom an initial position of the patient's teeth compared to thecomprehensive final position of the patient's teeth, a measure ofmisalignment for the patient's teeth, and a measure of a number ofaligner stages compared to a target number of aligner stages from theset of treatment details.
 22. The non-transient, computer-readablemedium of claim 16, wherein the program instructions are furtherconfigured to adjust the plurality of numerically expressed treatmenttargets into a plurality of adjusted numerically expressed treatmenttargets based on: the set of treatment details, the set of treatmentpreferences and the comprehensive final position of the patient's teeth;further wherein the program instructions are also further configured tocombine the plurality of numerically expressed treatment targets bycombining the plurality of adjusted numerically expressed treatmenttargets.
 23. The non-transient, computer-readable medium of claim 16,wherein the plurality of numeric limits comprises one or more of: amaximum velocity of tooth movement, a maximum amount of collisionbetween teeth, a tooth movement limitation, a maximum number of alignerstages, a maximum amount of occlusion, a maximum amount of occlusion, amaximum amount of overbite, a maximum amount of overjet, and a maximummidline position.
 24. The non-transient, computer-readable medium ofclaim 16, wherein the program instructions are further configured tominimize the single numerical function subject to the plurality ofnumeric limits using a constrained optimization method to get a solutionvector.
 25. The non-transient, computer-readable medium of claim 24,wherein the constrained optimization method comprises an interior pointmethod.
 26. The non-transient, computer-readable medium of claim 16,wherein the program instructions are further configured to map thesolution vector to a treatment plan by converting the solution vectorinto a set of key frames for each tooth, corresponding to a stagenumber, and positional information for each tooth, including an xcoordinate, a y coordinate, a z coordinate, and an angulation, aninclination and a rotation angle.
 27. The non-transient,computer-readable medium of claim 16, wherein the program instructionsare further configured to provide the final tooth position of thetreatment plan for display.